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Chapter 29
Electromagnetic Induction
and Faraday’s Law
Copyright © 2009 Pearson Education, Inc.
Faraday’s Law
dB
d
d


 
   A  B     A B cos  
dt
dt
dt
   IR
BUT  is NOT a conservative potential
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29-3 EMF Induced in a Moving
Conductor
This image shows another way the magnetic
flux can change:
R
Copyright © 2009 Pearson Education, Inc.
29-3 EMF Induced in a Moving
Conductor
 B  t   x  t  B; A outward
dB

  Bv I R
dt
Bv
I
R
I
2
 FI  I  B  I B   B  v
R
Copyright © 2009 Pearson Education, Inc.
ConcepTest 29.9 Motional EMF
A conducting rod slides on a
conducting track in a constant
1) clockwise
B field directed into the page.
2) counterclockwise
What is the direction of the
3) no induced current
induced current?
x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x
v
ConcepTest 29.9 Motional EMF
A conducting rod slides on a
conducting track in a constant
1) clockwise
B field directed into the page.
2) counterclockwise
What is the direction of the
3) no induced current
induced current?
The B field points into the page.
The flux is increasing since the
area is increasing. The induced
B field opposes this change and
therefore points out of the page.
Thus, the induced current runs
counterclockwise, according to
the right-hand rule.
x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x
v
x x x x x x x x x x x
Follow-up: What direction is the magnetic force on the rod as it moves?
29-3 EMF Induced in a Moving
Conductor
The induced emf has magnitude
This equation is valid as long as B, l, and
v are mutually perpendicular (if not, it is
true for their perpendicular components).
Copyright © 2009 Pearson Education, Inc.
29-3 EMF Induced in a Moving
Conductor
The induced current is in a direction that tends
to slow the moving bar
Conductor
_

w
_

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29-3 EMF Induced in a Moving
Conductor
Fe  e v  B  e v B  e Ee 
  v B w
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
w
29-3 EMF Induced in a Moving
Conductor
Example 29-6: Does a moving airplane develop a
large emf?
An airplane travels 1000 km/h in a region where the
Earth’s magnetic field is about 5 x 10-5 T and is
nearly vertical. What is the potential difference
induced between the wing tips that are 70 m apart?
Copyright © 2009 Pearson Education, Inc.
29-4 Electric Generators
A generator is the opposite of a motor – it
transforms mechanical energy into electrical
energy. This is an ac generator:
The axle is rotated by an
external force such as
falling water or steam.
The brushes are in
constant electrical
contact with the slip
rings.
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29-4 Electric Generators
If the loop is rotating with constant angular
velocity ω, the induced emf is sinusoidal:
For a coil of N loops,
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29-4 Electric Generators
Example 29-9: An ac generator.
The armature of a 60-Hz ac
generator rotates in a 0.15-T
magnetic field. If the area of the coil
is 2.0 x 10-2 m2, how many loops
must the coil contain if the peak
output is to be V0 = 170 V?
Copyright © 2009 Pearson Education, Inc.
29-4 Electric Generators
A dc generator is similar, except that it
has a split-ring commutator instead of slip
rings.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 29.10 Generators
A generator has a coil of wire
rotating in a magnetic field.
If the rotation rate increases,
1) increases
2) decreases
how is the maximum output
3) stays the same
voltage of the generator
4) varies sinusoidally
affected?
ConcepTest 29.10 Generators
A generator has a coil of wire
rotating in a magnetic field.
If the rotation rate increases,
1) increases
2) decreases
how is the maximum output
3) stays the same
voltage of the generator
4) varies sinusoidally
affected?
The maximum voltage is the leading
term that multiplies sin wt and is
given by e0 = NBAw. Therefore, if
w increases, then e0 must increase
as well.
e  NBA w sin( w t )
29-5 Back EMF and Counter Torque;
Eddy Currents
An electric motor turns because there is a
torque on it due to the current. We would
expect the motor to accelerate unless there is
some sort of drag torque.
That drag torque exists, and is due to the
induced emf, called a back emf.
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29-5 Back EMF and Counter Torque;
Eddy Currents
Example 29-10: Back emf in a
motor.
The armature windings of a
dc motor have a resistance of
5.0 Ω. The motor is connected
to a 120-V line, and when the
motor reaches full speed
against its normal load, the
back emf is 108 V. Calculate
(a) the current into the motor
when it is just starting up,
and (b) the current when the
motor reaches full speed.
Copyright © 2009 Pearson Education, Inc.
29-5 Back EMF and Counter Torque;
Eddy Currents
Conceptual Example 29-11: Motor overload.
When using an appliance such as a blender,
electric drill, or sewing machine, if the
appliance is overloaded or jammed so that
the motor slows appreciably or stops while
the power is still connected, the device can
burn out and be ruined. Explain why this
happens.
Copyright © 2009 Pearson Education, Inc.
29-5 Back EMF and Counter Torque;
Eddy Currents
A similar effect occurs in a generator – if it is
connected to a circuit, current will flow in it,
and will produce a counter torque. This
means the external applied torque must
increase to keep the generator turning.
Copyright © 2009 Pearson Education, Inc.
29-5 Back EMF and Counter Torque;
Eddy Currents
Induced currents can flow
in bulk material as well as
through wires. These are
called eddy currents, and
can dramatically slow a
conductor moving into or
out of a magnetic field.
Copyright © 2009 Pearson Education, Inc.
29-6 Transformers and Transmission
of Power
A transformer consists of two coils, either
interwoven or linked by an iron core. A
changing emf in one induces an emf in the
other.
The ratio of the emfs is equal to the ratio of
the number of turns in each coil:
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29-6 Transformers and Transmission
of Power
This is a step-up
transformer – the
emf in the secondary
coil is larger than the
emf in the primary:
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29-6 Transformers and Transmission
of Power
Energy must be conserved; therefore, in the
absence of losses, the ratio of the currents
must be the inverse of the ratio of turns:
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29-7 A Changing Magnetic Flux
Produces an Electric Field
A changing magnetic flux induces an electric
field; this is a generalization of Faraday’s
law. The electric field will exist regardless of
whether there are any conductors around:
.
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29-7 A Changing Magnetic Flux
Produces an Electric Field
Example 29-14: E produced by
changing B
B.
A magnetic field B between the pole
faces of an electromagnet is nearly
uniform at any instant over a circular
area of radius r0. The current in the
windings of the electromagnet is
increasing in time so that B changes in
time at a constant rate dB/dt
B at each
point. Beyond the circular region (r > r0),
we assume B
B = 0 at all times. Determine
the electric field E at any point P a
distance r from the center of the
circular area due to the changing B
B.
Copyright © 2009 Pearson Education, Inc.
HW # 10
Chapter 29 – 32, 38, 50, 70
Copyright © 2009 Pearson Education, Inc.