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Chapter 29
Electromagnetic
Induction
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 29
• To examine experimental evidence that a changing
magnetic field induces an emf
• To learn how Faraday’s law relates the induced emf to
the change in flux
• To determine the direction of an induced emf
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Goals for Chapter 29
• To calculate the emf induced by a moving conductor
• To learn how a changing magnetic flux generates an
electric field
• To study Maxwell’s Equations – the four fundamental
equations that describe electricity and magnetism
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Introduction
• How is a credit card reader
related to magnetism?
• Energy conversion makes
use of electromagnetic
induction.
• Faraday’s law and Lenz’s
law tell us about induced
currents.
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Induced current
• A changing magnetic flux causes an induced current.
No change => NO induced current!
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Induced current
• A changing magnetic flux causes an induced current.
The induced emf is the corresponding emf causing the current.
Copyright © 2012 Pearson Education Inc.
Induced current
• A changing magnetic flux causes an induced current.
The induced emf is the corresponding emf causing the current.
Copyright © 2012 Pearson Education Inc.
Induced current
• A changing magnetic flux causes an induced current.
The induced emf is the corresponding emf causing the current.
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Magnetic flux through an area element
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Faraday’s law
• Flux depends on orientation of surface with respect to B field.
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Faraday’s law
• Flux depends on orientation of surface with respect to B field.
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Faraday’s law
• Flux depends on orientation of surface with respect to B field.
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Faraday’s law
• Faraday’s law: Induced emf in a closed loop equals negative of
time rate of change of magnetic flux through the loop
 = –dB/dt
In this case, if the flux changed from maximum to
minimum in some time t, and loop was conducting,
an EMF would be generated!
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Faraday’s law
• Faraday’s law: Induced emf in a closed loop equals negative of
time rate of change of magnetic flux through the loop
 = –dB/dt
[B ]= Tesla-m2
[d B/ dt] = Tesla-m2/sec
and from F = qv x B
Teslas = Newtons-sec/Coulomb-meters [N/C][sec/meters]
[d B/ dt] = [N/C][sec/meter][m2/sec] = Nm/C
= Joule/C
= VOLT!
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Emf and the current induced in a loop
• Example 29.1: What is induced EMF & Current?
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Emf and the current induced in a loop
• Example 29.1: What is induced EMF & Current?
df/dt = d(BA)/dt = (dB/dt) A = 0.020 T/s x 0.012 m2
= 0.24 mV
I = E/R = 0.24 mV/5.0W = 0.048 mA
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Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Induced current
generates B field flux
opposing change
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Induced current
generates B field flux
opposing change
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Induced current
generates B field flux
opposing change
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Copyright © 2012 Pearson Education Inc.
Direction of the induced emf
• Direction of induced current from EMF creates B field to KEEP
original flux constant!
Induced current
generates B field flux
opposing change
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Lenz’s law
Lenz’s law:
The direction of any
magnetic induction effect is
such as to oppose the cause
of the effect.
Copyright © 2012 Pearson Education Inc.
Magnitude and direction of an induced emf
• Example 29.2 – 500 loop circular coil with radius
4.00 cm between poles of electromagnet. B field
decreases at 0.200 T/second. What are magnitude
and direction of induced EMF?
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Magnitude and direction of an induced emf
• Example 29.2 – 500 loop circular coil with radius
4.00 cm between poles of electromagnet. B field
decreases at 0.200 T/second. What are magnitude
and direction of induced EMF?
Careful with flux
ANGLE!
f between A and B!
 = –N dB/dt = [NdB/dt] x [A cos f]
Direction? Since B decreases, EMF resists change…
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A simple alternator – Example 29.3
• An alternator creates alternating
positive and negative currents
(AC) as a loop is rotated by an
external torque while in a fixed
magnetic field (or vice-versa!)
Note – w comes from an external
rotating force!
• Water turning a turbine
(hydroelectric)
• Gasoline Motor turning a shaft (AC
generator)
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A simple alternator – Example 29.3
• An alternator creates alternating
positive and negative currents
(AC) as a loop rotates in a fixed
magnetic field (or vice-versa!)
Note – NO commutator to reverse
current direction in the loop – so
you will get ALTERNATING
current
Copyright © 2012 Pearson Education Inc.
A simple alternator – Example 29.3
• An alternator creates alternating
positive and negative currents
(AC) as a loop rotates in a fixed
magnetic field (or vice-versa!)
For simple alternator rotating at
angular rate of w, what is the
induced EMF?
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A simple alternator
• Example 29.3: For simple alternator
rotating at angular rate of w, what is
induced EMF?
• B is constant; A is constant
• Flux B is NOT constant!
• B = BAcos f
• Angle f varies in time: f = wt
• EMF = - d [B ]/dt = -d/dt [BAcos(wt)]
• So EMF = wBAsin(wt)
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A simple alternator
• EMF = wBAsin(wt)
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DC generator and back emf in a motor
• Example 29.4: A DC generator creates ONLY onedirectional (positive) current flow with EMF always the
same “sign.”
Slip rings
AC alternator
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DC generator
DC generator and back emf in a motor
• Example 29.4: A DC generator creates ONLY onedirectional (positive) current flow with EMF always the
same “sign.”
Commutator
AC alternator
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DC generator
DC generator and back emf in a motor
• Commutator results in ONLY unidirectional (“direct”)
current flow:
EMF(DC gen) = | wBAsin(wt) |
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DC generator and back emf in a motor
• Example 29.4: A DC generator creates ONLY onedirectional (positive) current flow with EMF always the
same “sign.”
“Back EMF”
Generated from
changing flux
through the loop
DC generator
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DC generator and back emf in a motor
• Average EMF generated = AVG( | wBAsin(wt) | )
over Period T where T = 1/f = 2p/w
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DC generator and back emf in a motor
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DC generator and back emf in a motor
• Example 29.4: 500 turn coil, with sides 10 cm long,
rotating in B field of 0.200 T generates 112 V. What is w?
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Lenz’s law and the direction of induced current
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Lenz’s law and the direction of induced current
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Slidewire generator – Example 29.5
• What is magnitude and direction of induced emf?
Area A vector chosen to be into page
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Slidewire generator – Example 29.5
• B is constant; A is INCREASING => flux increases!
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Slidewire generator – Example 29.5
• Area A = Lx so dA/dt = L dx/dt = Lv
Width x
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Slidewire generator
• EMF = - d [B ]/dt = -BdA/dt = -BLv
Induced current creates B OUT of page
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Work and power in the slidewire generator
• Let resistance of wires be “R”
• What is rate of energy dissipation in circuit and rate of
work done to move the bar?
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Work and power in the slidewire generator
• EMF = -BLv
• I = EMF/R = -BLv/R
• Power = I2R = B2L2v2/R
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Work and power in the slidewire generator
• Work done = Force x Distance
• Power applied = Work/Time = Force x velocity
• Power = Fv = iLBv and I = EMF/R
• Power = (BLv/R)LBv = B2L2v2/R
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Motional electromotive force
• The motional electromotive force across the ends of a rod
moving perpendicular to a magnetic field is  = vBL.
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Motional electromotive force
• The motional electromotive force across the ends of a rod
moving perpendicular to a magnetic field is  = vBL.
• Across entire (stationary) conductor, E field will push current!
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Motional electromotive force
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Faraday disk dynamo
• Spinning conducting disc in uniform magnetic field.
• Generates current in connecting wires!
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Faraday disk dynamo
• Current increases with B, with Area, and with rotation rate w
• What is the EMF in terms of these variables?
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Faraday disk dynamo – does this violate Faraday’s Law?
• NO change in B field!
• NO change in Area!
• No change in flux?!!
• There should NOT be an
induced EMF??!
• But there IS!
• But if you rotate the
*magnet* instead, there
is NOT an EMF
• Shouldn’t it be relative?
!$%##
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Faraday disk dynamo – does this violate Faraday’s Law?
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Induced electric fields
• Wire loop around a solenoid
that experiences a changing
current.
• See a NEW current flow in
surrounding loop!
• But… the wire itself is NOT
in a B field (no “qv x B”
applies to make charges in
wire loop move!!
• AHA! Changing magnetic
flux causes an induced
electric field.
Copyright © 2012 Pearson Education Inc.
Induced electric fields
• Wire loop around a solenoid
that experiences a changing
current.
• See a NEW current flow in
surrounding loop!
• But… the wire itself is NOT
in a B field (no “qv x B”
applies to make charges in
wire loop move!!
• AHA! Changing magnetic
flux causes an induced
electric field.
Copyright © 2012 Pearson Education Inc.
Induced electric fields
Key – the integral path must
be stationary
And…
The E field created is NOT
conservative!
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