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Magnetism

�� Permanent magnet (compass Permanent magnet (compass needle) have been long used in needle) have been long used in navigational compasses.navigational compasses.

�� When the compass is placed on When the compass is placed on the horizontal surface, the the horizontal surface, the needle rotates until one end needle rotates until one end points to north.points to north.

�� The end of the needle that point The end of the needle that point north is label the north is label the north north magnetic polemagnetic pole the opposite the opposite end is the end is the south magnetic south magnetic pole.pole.

Magnets and Magnetic FieldsMagnets and Magnetic Fields

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Magnets and Magnetic Fields

• Like poles repel; unlike poles attract.

• The different between electric charge and magnetic poles is

1) We can separated +ve and –ve charge and produce isolated charge

2) We cannot separated magnetic poles.

Magnets and Magnetic Fields

However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

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Magnets and Magnetic FieldsMagnets and Magnetic Fields

�� Magnetic field exist Magnetic field exist surround a magnet.surround a magnet.

�� Magnetic field have Magnetic field have magnitude and magnitude and directiondirection

�� The direction of The direction of magnetic field is the magnetic field is the direction that a direction that a compass needle compass needle pointspoints

Magnets and Magnetic Fields

The Earth’s magnetic field is similar to that of a bar magnet.

Note that the Earth’s “North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it.

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Magnets and Magnetic Fields

A uniform magnetic field is constant in magnitude and direction.

The field between these two wide poles is nearly uniform.

Electric Currents Produce Magnetic Fields

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•• ThisThis experimentexperiment showsshows thatthat anan electricelectriccurrentcurrent producesproduces aa magneticmagnetic fieldfield..

•• TheThe directiondirection ofof thethe fieldfield isis givengiven byby aa rightright--handhand rulerule..

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Electric Currents Produce Magnetic Fields

Force on an Electric Current in a Magnetic Field; Definition of B

A magnet exerts a force on a current-carryingwire. The direction of the force is given by aright-hand rule.

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Force on an Electric Current in a Magnetic Field; Definition of B

The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation.

(20-1)

This equation defines the magnetic field B.

Force on an Electric Current in a Magnetic Field; Definition of B

Unit of B: the tesla, T.

1 T = 1 N/A·m.

Another unit sometimes used: the gauss (G).

1 G = 10-4 T.

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Force on Electric Charge Moving in a Magnetic Field

The force on a moving charge is related to the force on a current:

(20-3)

Once again, the direction is given by a right-hand rule.

Force on Electric Charge Moving in a Magnetic Field

If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle.

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Force on Electric Charge Moving in a Magnetic Field

Problem solving: Magnetic fields – things to remember

1. The magnetic force is perpendicular to the magnetic field direction.

2. The right-hand rule is useful for determining directions.

3. Equations in this chapter give magnitudes only. The right-hand rule gives the direction.

Force on Electric Charge Moving in a Magnetic Field

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Magnetic Field Due to a Long Straight Wire

The field is inversely proportional to the distance from the wire:

(20-6)

The constant µ0 is called the permeability of free space, and has the value:

Force between Two Parallel Wires

The magnetic field producedat the position of wire 2 due tothe current in wire 1 is:

The force this field exerts on a length l2 of wire 2 is:

(20-7)

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Force between Two Parallel Wires

Parallel currents attract; antiparallel currents repel.

Solenoids and Electromagnets

A solenoid is a long coil of wire. If it is tightlywrapped, the magnetic field in its interior is almostuniform:

(20-8)

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Solenoids and Electromagnets

If a piece of iron is inserted in the solenoid, the magnetic

field greatly increases. Such electromagnets have many

practical applications.

AmpAmpère’s Lawère’s Law �� AndreAndre--MarieMarie AmpèreAmpère FrenchFrench PhysicistPhysicist((17751775––18361836))

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Ampère’s Law

Ampère’s law relates themagnetic field around aclosed loop to the totalcurrent flowing through theloop.

(20-9)

Ampère’s Law

Ampère’s law can be used to calculate themagnetic field in situations with a high degreeof symmetry.

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Torque on a current loop in a Torque on a current loop in a uniform magnetic fielduniform magnetic field

�� Torque produced on a current loop in Torque produced on a current loop in magnetic field because magnetic force magnetic field because magnetic force producedproduced

�� Consider a rectangular loop carrying a Consider a rectangular loop carrying a current current II in the presence of a uniform in the presence of a uniform magnetic field directed parallel to the magnetic field directed parallel to the plane of the loop.plane of the loop.

(a)(a)OverheadOverhead viewview ofof aa rectangularrectangular currentcurrent

looploop inin aa uniformuniform magneticmagnetic fieldfield.. NoNo

forcesforces areare actingacting onon sidessides ((11)) andand ((33))

becausebecause thesethese sidessides areare parallelparallel toto BB..

ForcesForces areare actingacting onon sidessides ((22)) andand ((44))..

(a)(a)EdgeEdge viewview ofof thethe looploop sightingsighting downdown

sidessides andand showsshows thatthat thethe forcesforces FF22 andand

FF44 exertedexerted onon thesethese sidessides createcreate aa torquetorque

thatthat tendstends toto twisttwist thethe looploop clockwiseclockwise..

TheThe purplepurple dotdot inin thethe leftleft circlecircle

representsrepresents currentcurrent inin wirewire comingcoming

towardtoward youyou;; thethe purplepurple crosscross inin thethe rightright

circlecircle representsrepresents currentcurrent inin wirewire movingmoving

awayaway fromfrom youyou..

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The magnitude of force acting on sides (2) The magnitude of force acting on sides (2)

and (4):and (4):

FF22 = F= F44 = IaB= IaB

if loop is pivoted so that can rotate about if loop is pivoted so that can rotate about

point O, these two forces will produce a point O, these two forces will produce a

torque about point O that will cause the torque about point O that will cause the

loop to rotate clockwise.loop to rotate clockwise.

IabB2

b(IaB)

2

b(IaB)

2

bF

2

bFτ 42max =+=+=

Since area of loop Since area of loop A =abA =ab, ,

then then ττmaxmax = IAB= IAB

Maximum torque, when magnetic field Maximum torque, when magnetic field

parallel to plane of loop.parallel to plane of loop.

If current reversed, rotation counter If current reversed, rotation counter

clockwise.clockwise.

If uniform magnetic field makes an angle If uniform magnetic field makes an angle

θθ < 90< 90oo with a line perpendicular to the with a line perpendicular to the

plane of the loopplane of the loop

The magnitude of the net torque about O:The magnitude of the net torque about O:

IABsinθτ

IabBsinθτ

sinθ2

bIaBsinθ

2

bIaBτ

sinθ2

bsinθ

2

bFτ 42

=

=

+

=

+= F

Max torque value when field is perpendicular to normal of loop’s plane, Max torque value when field is perpendicular to normal of loop’s plane,

that is that is θθ = 90= 90oo , and torque is zero when field is parallel to normal of , and torque is zero when field is parallel to normal of

loop’s plane, that is loop’s plane, that is θθ = 0= 0oo..

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Torque on a Current Loop; Magnetic Moment

The forces on opposite sides of a current loop willbe equal and opposite (if the field is uniform andthe loop is symmetric), but there may be a torque.

The magnitude of the torque is given by:

(20-10)

The quantity NIA is called the magnetic dipolemoment, M:

(20-11)

Example Example –– Torque on a coilTorque on a coil

A circular coil of wire has a diameter of 20 cm and contains 10 loops. A circular coil of wire has a diameter of 20 cm and contains 10 loops. The current in each loops is 3.0 A and the coil is placed in a 2.0 T The current in each loops is 3.0 A and the coil is placed in a 2.0 T external magnetic field. Determine the maximum and minimum torque external magnetic field. Determine the maximum and minimum torque exerted on the coil by the field. exerted on the coil by the field.

Solution: Solution:

The area of 1 loop of the coil is: The area of 1 loop of the coil is:

A=A=ππrr22= = ππ(0.100m)(0.100m)22 = 3.14 x 10= 3.14 x 10--2 2 mm22

The maximum torque occurs when the coil’s face is parallelThe maximum torque occurs when the coil’s face is parallel

to the magnetic field, to the magnetic field, θθ=90=9000. sin 90. sin 9000=1=1

= (10)(3A)(3.14x10= (10)(3A)(3.14x10--22)(2 T)(1)=1.88N.m)(2 T)(1)=1.88N.m

The minimum torque occurs if sinThe minimum torque occurs if sinθθ=0 for which =0 for which θθ=0=000 and the torque = 0and the torque = 0

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Applications: Motors

An electric motor also takes advantage of thetorque on a current loop, to change electricalenergy to mechanical energy.

Summary

• Magnets have north and south poles

• Like poles repel, unlike attract

• Unit of magnetic field: tesla

• Electric currents produce magnetic fields

• A magnetic field exerts a force on an electric current:

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Summary

• A magnetic field exerts a force on a moving charge:

• Magnitude of the field of a long, straight current-carrying wire:

• Parallel currents attract; antiparallel currents repel

Summary

• Magnetic field inside a solenoid:

• Ampère’s law:

• Torque on a current loop: