11

BENE 1113BENE 1113PRINCIPLES OF ELECTRICAL AND PRINCIPLES OF ELECTRICAL AND

ELECTRONICSELECTRONICS

CHAPTER 2CHAPTER 2

MAGNETIC AND MAGNETIC AND ELECTROMAGNETICELECTROMAGNETIC

22

TOPICS COVEREDTOPICS COVERED

bull MAGNETIC UNITSMAGNETIC UNITS

bull POLES OF MAGNETPOLES OF MAGNET

bull MAGNETIC FIELDMAGNETIC FIELD

bull ELECTROMAGNETISMELECTROMAGNETISM

bull ELECTROMAGNETIC INDUCTIONELECTROMAGNETIC INDUCTION

bull RIGHT HAND RULERIGHT HAND RULE

bull FLEMING LEFT HAND RULEFLEMING LEFT HAND RULE

bull FARADAYrsquoS LAWFARADAYrsquoS LAW

bull LENZrsquoS LAWLENZrsquoS LAW

3

INTRODUCTION

bull The first experience with magnetism occurred when pieces of stone were found to have the ability to attract iron or similar materials These stones were called magnets

bull Magnetic forces are refer to the force that acts between magnets and magnetic materials

-There are two types of magnetic poles conventionally called North and South

-Like poles repel and opposite poles attract

4

INTRODUCTION

bull Magnetic fields are described by drawing flux lines that represent the magnetic field

bull Each of magnetic flux line travels from the north pole to the south pole thro space

bull The line returns to the north pole thro the magnet itself

Where lines are close together the flux density is higher

Where lines are further apart the flux density is lower

bull Magnetic flux lines are invisible but the effects can be visualized with iron filings sprinkled in a magnetic field

5

INTRODUCTION

6

LAWS OF MAGNETISM

1 Like poles repel each other

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

22

TOPICS COVEREDTOPICS COVERED

bull MAGNETIC UNITSMAGNETIC UNITS

bull POLES OF MAGNETPOLES OF MAGNET

bull MAGNETIC FIELDMAGNETIC FIELD

bull ELECTROMAGNETISMELECTROMAGNETISM

bull ELECTROMAGNETIC INDUCTIONELECTROMAGNETIC INDUCTION

bull RIGHT HAND RULERIGHT HAND RULE

bull FLEMING LEFT HAND RULEFLEMING LEFT HAND RULE

bull FARADAYrsquoS LAWFARADAYrsquoS LAW

bull LENZrsquoS LAWLENZrsquoS LAW

3

INTRODUCTION

bull The first experience with magnetism occurred when pieces of stone were found to have the ability to attract iron or similar materials These stones were called magnets

bull Magnetic forces are refer to the force that acts between magnets and magnetic materials

-There are two types of magnetic poles conventionally called North and South

-Like poles repel and opposite poles attract

4

INTRODUCTION

bull Magnetic fields are described by drawing flux lines that represent the magnetic field

bull Each of magnetic flux line travels from the north pole to the south pole thro space

bull The line returns to the north pole thro the magnet itself

Where lines are close together the flux density is higher

Where lines are further apart the flux density is lower

bull Magnetic flux lines are invisible but the effects can be visualized with iron filings sprinkled in a magnetic field

5

INTRODUCTION

6

LAWS OF MAGNETISM

1 Like poles repel each other

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

3

INTRODUCTION

bull The first experience with magnetism occurred when pieces of stone were found to have the ability to attract iron or similar materials These stones were called magnets

bull Magnetic forces are refer to the force that acts between magnets and magnetic materials

-There are two types of magnetic poles conventionally called North and South

-Like poles repel and opposite poles attract

4

INTRODUCTION

bull Magnetic fields are described by drawing flux lines that represent the magnetic field

bull Each of magnetic flux line travels from the north pole to the south pole thro space

bull The line returns to the north pole thro the magnet itself

Where lines are close together the flux density is higher

Where lines are further apart the flux density is lower

bull Magnetic flux lines are invisible but the effects can be visualized with iron filings sprinkled in a magnetic field

5

INTRODUCTION

6

LAWS OF MAGNETISM

1 Like poles repel each other

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

4

INTRODUCTION

bull Magnetic fields are described by drawing flux lines that represent the magnetic field

bull Each of magnetic flux line travels from the north pole to the south pole thro space

bull The line returns to the north pole thro the magnet itself

Where lines are close together the flux density is higher

Where lines are further apart the flux density is lower

bull Magnetic flux lines are invisible but the effects can be visualized with iron filings sprinkled in a magnetic field

5

INTRODUCTION

6

LAWS OF MAGNETISM

1 Like poles repel each other

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

bull Magnetic flux lines are invisible but the effects can be visualized with iron filings sprinkled in a magnetic field

5

INTRODUCTION

6

LAWS OF MAGNETISM

1 Like poles repel each other

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

6

LAWS OF MAGNETISM

1 Like poles repel each other

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

7

LAWS OF MAGNETISM

2 Unlike poles attract each other

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

8

LAWS OF MAGNETISM

bull 3 The attractiverepelling force increases as the distance between the magnet decreasesndash To demonstrate this law one bar magnet is placed on the table

By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table

ndash When the two magnets become closer enough the magnet on the table will be drawn to the second magnet

ndash When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table the first magnet slides toward the second

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

Magnetic attraction and repulsion

9

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

10

Lines of force tend to take the path of least magneticresistance This fact introduces two features

- The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized

- When a material that can be magnetized is placed within the magnetic field the path of some of the lines of force is distorted in order to pass through this material

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

11

NON MAGNETIC MATERIALS

bull Materials that have no obvious magnetic properties

bull Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out

bull Non magnetic material such as paper glass wood and plastic

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

12

PERMANENT MAGNET

bull Magnets made of steel alloys hold their magnetism for a long period of time That is called permanent magnet

bull Magnetic fields of the individual atom are aligned in one preferred direction giving rise to a net magnetic field

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

13

MAGNETIC MATERIALS

bull Materials respond differently to the force of a magnetic fieldndash A magnet strongly attract Ferromagnetic materialsndash A magnet weakly attract Paramagnetic materialsndash A magnet weakly repel Diamagnetic materials

bull The orientation of the spin of the electrons in an atom the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field

the responds to magnetic field that substance become magnetized (to become a magnet)

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

bull Ferromagnetic Material ndash A material easy to magnetize (ie Iron Steel Cobalt Perm-alloy and Alnico)

bull Paramagnetic Material- A material that can be slightly magnetized

bull Diamagnetic Material ndash A material that is difficult to magnetize

MAGNETIC MATERIALMAGNETIC MATERIALS

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

15

FERROMAGNETIC MATERIALS

bull There are domains in which the magnetic fields of the individual atoms align but the orientation of the magnetic fields of the domains is random

bull This offer no net magnetic field

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

16

bull A useful property of ferromagnets is that when an external magnetic field is applied to them the magnetic fields of the individual domains tend to line up in the direction of this external field due to the nature of the magnetic forces

bull This cause the external magnetic field to be enhanced

bull Ferromagnet material such as iron nickel and cobalt

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

17

MAGNETIC MATERIALS

bull Paramagnetic materialsndash Weakly attracted to magnetic fieldndash Aluminum and copperndash These materials can be a magnet but their attractive

force can only be measured with sensitive instruments

ndash The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force

ndash Sometimes this materials are typically considered as non magnetic materials

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

18

MAGNETIC MATERIALS

bull Diamagnetic materialndash Means that when they are located at the

strong magnetic field they induce a weak magnetic force in the opposite direction

ndash In other words they weakly repel a strong magnet

ndash Bismuth and carbon graphite are the strongest diamagnetic followed by mercury silver water diamonds wood and living tissues

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

Magnetic Flux

bull The unit of magnetic flux is weber (Wb)

bull One weber equals 1x108 lines of magnetic flux

bull The weber is a very large unit thus microweber (μWb) is used

bull 1 μWb equals 100 lines of magnetic flux

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

20

MAGNETIC UNITS

1 Flux Densitybull Is the amount of flux per unit area bull Symbolized by Bbull Unit tesla (T) or Wb m2

bull 1 Wbm2 = tesla

AB

where is the flux (group of 1x108 lines of force)

A is the cross-sectional area in m2

The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux The strength of a magnetic field can be determined by the flux density

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

Example 1

bull Compare the flux and the flux density in the two magnetic cores shown in Figure below The diagram represents the cross section of a magnetized material Assume that each dot represents 100 lines or 1 μWb

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

22

Example 2

bull What happens to the flux density if the same flux shown in the first figure is in a core of 50cm x 50cm

bull If the flux density in a certain magnetic material is 023T and the area of the material is 038in2 what is the flux through the material

bull Calculate B if A = 005 in2 and Φ = 1000μWb

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

23

ELECTROMAGNETISM

bull Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it

bull When electricity passed through a wire a magnetic field is created around the wire in a specific direction The magnetic field disappears when the current flow stop

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

24

Visible affects of an electromagnetic field

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

25

ELECTROMAGNETISM

Right Hand Rulebull To find the direction of the magnetic

field bull The field strength is not uniform

throughout the magnetic field the further away from the conductor the weaker the field intensity

bull The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

26

Electromagnetic Properties 1Permeability (μ)

ndash The ability of a material to establish a magnetic fieldndash The higher the permeability the more easily a

magnetic field can be established

ndash The permeability of a vacuum (μ0) is 4πX10-7 WbAtm (Webersampere-turnmeter)

ndash The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum

0r

Unit is dimensionless

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

27

Electromagnetic Properties

2Reluctance ( )ndash The opposition to the establishment of a

magnetic field in a materialndash The value of reluctance is directly proportional

to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material as expressed by the following equation

l

A Unit is AtWb

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

28

Example 3

bull Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel The inner radius of the torus is 175cm and the outer radius of the torus is 225 cm Assume the permeability of low carbon steel is 2 x 10-4 WbAtm

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

29

Example 4

bull Mild steel has a relative permeability of 800 Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 10cm x 12 cm

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

Example 5

bull A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 05cm air gap at one of its side It has a relative permeability of 6000The cross section is 2cm by 3cmCalculate the reluctance of the core and the gap

30

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

31

Electromagnetic Properties

3Magnetomotive Force (mmf)ndash Current in a conductor produces a magnetic field

The cause of the magnetic field is called the magnetomotive force (mmf)

ndash The unit of mmf is ampere-turn (At)ndash The formula for mmf is

where Fm is the magnetomotive force N is the number of turns of wire and I is the current in amperes

mF NI

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

32

Electromagnetic PropertiesFigure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by

mF

This equation is known as Ohmrsquos Law for magnetic circuits since Φ is analogous to current the mmf (Fm) is analogous to voltage and reluctance (R) is analogous to resistance

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

33

OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS

bull Ohmrsquos Law when applied to electrical circuits gave the formula

I=VR(21)

where I = current flow in amperes

V = electromotive forcevoltage

R = current flow oppositionresistance

bull A similar version can be applied to magnetic circuits that is

(22)

where = magnetic flow of lines of force (webers)

Fm = magnetomitive force (ampere-turns)

R = magnetic reluctance (NI Wb)

mF

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

34

MAGNETIC UNITS

bull From Eq 22 it can be seen that increasing either the current or turns of a solenoid will increase the flux

bull A decreases in R would also increases the fluxbull Ohmrsquos Law for magnetic circuits may be given in three variations to suit particular

problems

bull For Electrical Equivalent)(

)(

)(

turnsAmpereRNI

WbAtNI

R

webersR

NI

m

m

m

IRVI

VR

R

VI

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

35

MAGNETIC UNIT

1 Magnetizing Force (Magnetic Field Intensity) H bull The mmf required to magnetize a unit length of a

magnetic pathbull The unit is expressed in ampere-turns per metre

(At m) and the symbol is H

where H = magnetizing force or magnetic field intensity

NI = Ampere turns

l = length between poles of the coil

l

NI

l

FH m

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

RELATIONSHIP BETWEEN B amp H

bull When the magnetomotive force Fm increases the magnetizing force H increases

bull At the same time the flux increases since

bull The flux density also increases as

bull In other word B is also proportional to H

B HB H = Constant =

36

mF

AB

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

37

bull The ratio BH in a material is always constant and is equal to the absolute permeability of the material (= o r)

bull ObviouslyB = orH (in medium)

B = oH (in air)

RECALLμ = relative abilityof substance to conduct magnetic lines of force as compared with air

RELATIONSHIP BETWEEN B amp H

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

38

Example 5

bull How much flux is established in the magnetic path of Figure below if the reluctance of the material is 28 x 105

AtWb

Figure 10-12

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

39

Example 6

bull There is 85mA of current through a coil with 500 turnsndash What is mmfndash What is the reluctance of the circuit in the flux

is 500 μWb

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

40

EXERCISE

1 An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units Calculate the flux produced when 10 A flows through the coil

2 A contractor coil has 7200 turns which are wound on iron core rectangular in section and having cross-sectional dimension of 20mm x 30 mm If the flux density in the magnetic circuit is 12 Tesla find the reluctance of the magnetic core The current drawn is 01 A

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

41

POLES OF A MAGNET

bull The points about the poles of a magnet(i) The poles of a magnet cannot be

separated If a bar magnet is broken into two parts each

part will be a complete magnet with poles at its ends No matter how many times a magnet is broken each

piece will contain n-pole at one end and s-pole at the other

(ii) The two poles of a magnet are equal in strength- The force between two magnetic poles is directly

proportional to the product of their poles strengths and inversely proportional to the square of distance between them

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

42

ELECTROMAGNETIC INDUCTION

bull When there is a relative motion between a conductor and a magnetic field a voltage is produced across the conductor

bull This principal is known as electromagnetic induction and the resulting voltage is induced voltage

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

ELECTROMAGNETIC INDUCTION

43

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

44

ELECTROMAGNETIC INDUCTION

bull When a current carrying conductor is placed at right angles to a magnetic field it experiences a mechanical force F given by

where B = flux density in wbm2

I = current through conductor in ampere

= length of conductor metres

bull The direction of this force can be found by Flemingrsquos Left-hand rule

BIlF

l

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

45

ELECTROMAGNETIC INDUCTION

Faradayrsquos Law1 The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic field with respect to the coil

(a) (b)

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

46

2 The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N)

(a) (b)

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

47

ELECTROMAGNETIC INDUCTION

Faradayrsquos LawFaradayrsquos Law state that

The voltage induced across a coil of wire equals the number of turns in the coil times the rate of

change of the magnetic flux

dt

dNvind

In mathematic

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

48

ELECTROMAGNETIC INDUCTION

Lenzrsquos Lawbull Lenzrsquos Law is used to find the direction of induced

emf and hence current in a conductor or coil

bull Lenzrsquos Law is stated as follows

The direction of the induced current is such as to oppose the change causing it

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

49

ELECTROMAGNETIC INDUCTION

bull LENZrsquoS LAWbull The diagram shows the north

pole of a bar magnet approaching a solenoid

bull According to Lenzs law the current which is generated in the coil must opposes the approaching magnetic field

bull This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet as the induced north pole tends to repel the approaching north pole

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

50

ELECTROMAGNETIC INDUCTION

bull The diagram shows the north pole of a bar magnet withdrawing from a solenoid

bull According to Lenzs law the current which is generated in the coil must oppose the departing magnetic field

bull This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing

magnet as the induced south pole tends to attract the departing north pole

Lenzrsquos Law

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51

5151

THANK THANK YOUYOU

• Slide 1
• TOPICS COVERED
• INTRODUCTION
• Slide 4
• Slide 5
• LAWS OF MAGNETISM
• Slide 7
• Slide 8
• Magnetic attraction and repulsion
• Slide 10
• NON MAGNETIC MATERIALS
• PERMANENT MAGNET
• MAGNETIC MATERIALS
• MAGNETIC MATERIAL
• FERROMAGNETIC MATERIALS
• Slide 16
• Slide 17
• Slide 18
• Magnetic Flux
• MAGNETIC UNITS
• Example 1
• Example 2
• ELECTROMAGNETISM
• Slide 24
• Slide 25
• Electromagnetic Properties
• Slide 27
• Example 3
• Example 4
• Example 5
• Slide 31
• Electromagnetic Properties
• OHMrsquoS LAW APPLIED TO MAGNETIC CIRCUITS
• Slide 34
• MAGNETIC UNIT
• RELATIONSHIP BETWEEN B amp H
• Slide 37
• Slide 38
• Example 6
• EXERCISE
• POLES OF A MAGNET
• ELECTROMAGNETIC INDUCTION
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51