lecture4 (chap 4)
TRANSCRIPT
7/28/2019 Lecture4 (Chap 4)
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Topic 4 : MAGNETIC FORCES AND MAGNETIC FIELDS
• Magnetic Fields
• The Force that a Magnetic Field Exerts on a Moving
Charge
• The Motion of a Charged Particle in a Magnetic Field
• The Force on a Current in a Magnetic Field
• The Torque on a Current-Carrying Coil
• Magnetic Field Produced by Currents
• Ampere’s Law
• Electromagnetic Induction
• Mutual-Inductance and Self-Inductance
• Transformer
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21.1 Magnetic Fields
The needle of a compass is permanent magnet that has a northmagnetic pole (N) at one end and a south magnetic pole (S) at
the other.
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21.1 Magnetic Fields
The behavior of magnetic
poles is similar to that of
like and unlike electric charges.
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21.1 Magnetic Fields
Surrounding a magnet there is a magnetic f ie ld . The direction
of the magnetic field at any point in space is the direction indicated
by the north pole of a small compass needle placed at that point.
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21.1 Magnetic Fields
The magnetic field lines and pattern of iron filings in the vicinity of a
bar magnet and the magnetic field lines in the gap of a horseshoe
magnet.
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21.2 The Force That a Magnetic Field Exerts o n a Charge
The following conditions must be met for a charge to experience
a magnetic force when placed in a magnetic field:
1. The charge must be moving.
2. The velocity of the charge must have a component that is
perpendicular to the direction of the magnetic field.
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21.2 The Force That a Magnetic Field Exerts o n a Charge
Righ t Hand Ru le No. 1. Extend the right hand so the fingers point
along the direction of the magnetic field and the thumb points along
the velocity of the charge. The palm of the hand then faces in the
direction of the magnetic force that acts on a positive charge.
If the moving charge is negative,
the direction of the force is opposite
to that predicted by RHR-1.
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21.2 The Force That a Magnetic Field Exerts o n a Charge
DEFINITION OF THE MAGNETIC FIELD
The magnitude of the magnetic field at any point in space is definedas
sinvq
F B
o
where the angle (0<θ<180o) is the angle between the velocity of
the charge and the direction of the magnetic field.
SI Unit o f Magnetic Field: Ttesla1
meter coulomb
secondnewton
tesla10gauss1 4
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21.2 The Force That a Magnetic Field Exerts o n a Charge
Example 1 Magnetic Forces on Charged Particles
A proton in a particle accelerator has a speed of 5.0x106 m/s. The proton
encounters a magnetic field whose magnitude is 0.40 T and whose directionmakes and angle of 30.0 degrees with respect to the proton’s velocity
(see part (c) of the figure). Find (a) the magnitude and direction of the
force on the proton and (b) the acceleration of the proton. (c) What would
be the force and acceleration of the particle were an electron?
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21.2 The Force That a Magnetic Field Exerts o n a Charge
N106.1
0.30sinT40.0sm100.5C1060.1sin
13
619
vBq F o(a)
(b)
(c)
213
27
13
p
sm106.9kg1067.1
N106.1
m
F a
Magnitude is the same, but direction is opposite.
217
31
13
e
sm108.1kg1011.9
N106.1
m
F a
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21.3 The Motion of a Charged Part icle in a Magnetic Field
Conceptual Examp le 2 A Velocity Selector
A velocity selector is a device for measuring
the velocity of a charged particle. The device
operates by applying electric and magnetic
forces to the particle in such a way that these
forces balance.
How should an electric field be applied so that
the force it applies to the particle can balance
the magnetic force?
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Exercise 1
Find the direction of the magnetic field acting on the
positively charged particle moving in the various
situations shown in figure below, if the direction of the
magnetic force acting on it is as indicated.
Into the page Towards bottom of the pageTowards the right
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21.3 The Motion of a Charged Part icle in a Magnetic Field
The electrical force can do work on a
charged particle.
The magnetic force cannot do work on a
charged particle.
C
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21.5 The Force on a Curren t in a Magnetic Field
The magnetic force on the
moving charges pushes the
wire to the right.
21 5 Th F C t i M ti Fi ld
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21.5 The Force on a Curren t in a Magnetic Field
sinqvB F
sin Bt vt
q
F L
I
sin ILB F
21 5 Th F C t i M ti Fi ld
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21.5 The Force on a Curren t in a Magnetic Field
Example 5 The Force and Acceleration in a Loudspeaker
The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of
wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is2.0 A. (a) Determine the magnetic force that acts on the coil and the
cone. (b) The voice coil and cone have a combined mass of 0.0200 kg. Find
their acceleration.
21 5 Th F C t i M ti Fi ld
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21.5 The Force on a Curren t in a Magnetic Field
(a)
N86.0
90sinT10.0m0025.055A0.2
sin
ILB F
(b)2sm43
kg020.0
N86.0
m
F a
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Exercise 2
A current I = 15 A is directed along the positive x axis
and perpendicularly to a magnetic field. The conductor
experiences a magnetic force per unit length of 0.12 N/m
in the negative y direction. Calculate the magnitude and
direction of the magnetic field in the region throughwhich the current passes.
The direction of B:
0.12 N m
sin 15 A sin90
F LB
I
38.0 10 T
the directionz
21 6 The Torq ue on a Current Carrying Co il
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21.6 The Torq ue on a Current-Carrying Co il
The two forces on the loop have equal magnitude but an application
of RHR-1 shows that they are opposite in direction.
21 6 The Torq ue on a Current Carrying Co il
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21.6 The Torq ue on a Current-Carrying Co il
The loop tends to rotate such that its
normal becomes aligned with the magneticfield.
21 6 The Torq ue on a Current Carrying Co il
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21.6 The Torq ue on a Current-Carrying Co il
sinsinsin Net torque21
21 IABw ILBw ILB
sin
momentmagnetic
B NIA
number of turns of wire
21 6 The Torq ue on a Current Carrying Co il
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21.6 The Torq ue on a Current-Carrying Co il
Examp le 6 The Torque Exerted on a Current-Carrying Coil
A coil of wire has an area of 2.0x10-4m2, consists of 100 loops or turns,
and contains a current of 0.045 A. The coil is placed in a uniform magnetic
field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil.
(b)Find the maximum torque that the magnetic field can exert on the
coil.
(a)
2424
momentmagnetic
mA100.9m100.2A045.0100 NIA
m N104.190sinT15.0mA100.9sin 424
momentmagnetic
B NIA(b)
21 7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
Righ t-Hand Ru le No. 2. Curl the fingers of the
right hand into the shape of a half-circle. Point
the thumb in the direction of the conventional
current, and the tips of the fingers will point
in the direction of the magnetic field.
21 7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
A LONG, STRAIGHT WIRE
r
I B
o
2
AmT104 7 o
permeability of
free space
21 7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
Example 7 A Current Exerts a Magnetic Force on a Moving Charge
The long straight wire carries a current
of 3.0 A. A particle has a charge of
+6.5x10-6 C and is moving parallel to
the wire at a distance of 0.050 m. The
speed of the particle is 280 m/s.
Determine the magnitude and direction
of the magnetic force on the particle.
21 7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
sin2
sin
r
I qvqvB F o
r
I B
o
2
21 7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
Current carrying wires can exert forces on each other.
21.7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
Conceptual Examp le 9 The Net Force That a Current-Carrying Wire
Exerts on a Current Carrying Coil
Is the coil attracted to, or repelled by the wire?
21.7 Magnet ic Fie lds Produc ed by Currents
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21.7 Magnet ic Fie lds Produc ed by Currents
A LOOP OF WIRE
center of circular loop
R
I B
o
2
21.7 Magnet ic Fie lds Produc ed by Currents
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g y
The field lines around the bar magnet resemble those around the loop.
21.7 Magnet ic Fie lds Produc ed by Currents
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g y
21.7 Magnet ic Fie lds Produc ed by Currents
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g y
A SOLENOID
Inter ior of a soleno id nI B o
number of turns per
unit length
21.8 Ampere’s Law
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p
AMPERE’S LAW FOR STATIC MAGNETIC FIELDS
For any current geometry that produces a
magnetic field that does not change in time,
I B o ||
net current
passing through
surface bounded
by path
21.8 Ampere’s Law
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p
Examp le 11 An Infinitely Long, Straight, Current-Carrying Wire
Use Ampere’s law to obtain the magnetic field.
I B o ||
I B o
I r B o 2
r
I B
o
2
22.1 Induc ed Emf and Induced Current
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There are a number of ways a magnetic field can be used to
generate an electric current.
It is the changing field that produces the current.
22.1 Induc ed Emf and Induced Current
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The current in the coil is called the induced cu rrent because it is brought
about by a changing magnetic field.
Since a source emf is always needed to produce a current, the coil behavesas if it were a source of emf. This emf is known as the induced emf.
The phenomena of producing an induced emf with the aid of a magnetic
field is called electromagnet ic induct ion.
22.8 Mutual Inductance and Sel f Indu ctance
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MUTUAL INDUCTANCE
The changing current in the primary coil creates a changing
magnetic flux through the secondary coil, which leads to an
induced emf in the secondary coil.
The effect in called
mu tual induct ion.
22.8 Mutual Inductance and Sel f Indu ctance
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Emf due to mutual induct ion
t
I M S
p
mutual inductance
SI Unit of mutual inductanc e: (Henry) H1As1V
t
N s
sS
22.8 Mutual Inductance and Sel f Indu ctance
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SELF INDUCTANCE
The effect in which a changing current in a circuit induces and emf
in the same circuit is referred to as sel f induct ion .
22.8 Mutual Inductance and Sel f Indu ctance
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SI Unit of self ind uctanc e: (Henry) H1As1V
t
I L
self inductance
22.8 Mutual Inductance and Sel f Indu ctance
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THE ENERGY STORED IN AN INDUCTOR
Energy stored in
an induc tor
Energy density
2
21Energy LI
2
2
1densityEnergy B
o
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Exercise 3
A coil of wire with a resistance of 0.45 has a
self-inductance of 0.083 H. If a 6.0-V battery is
connected across the ends of the coil and the
current in the circuit reaches an equilibriumvalue, what is the stored energy in the inductor?
Answer: 7.38 J
22.9 Transformers
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A t ransformer is a device for increasing or decreasing an ac
voltage.
t N
ss
t N
p p
p
s
p
s
N
N
p
s
N
N turns ratio
22.9 Transformers
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p
s
p
s
N
N
V
V
Transformer
equat ion
22.9 Transformers
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s
p
s
p
p
s
N
N
V
V
I
I
A transformer that steps up the voltage simultaneously steps
down the current, and a transformer that steps down the voltage
steps up the current.
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Exercise 4
A transformer changes 120 V across the
primary to 1200 V across the secondary.
If the secondary coil has 800 turns, how
many turns does the primary coil have?
Answer: 80