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Electromagnetic Induction
What’s Next?
Electromagnetic Induction
 Faraday’s Discovery
 Electromotive Force
 Magnetic Flux
 Electric Generators
 Lenz’s Law
 Self-Inductance
 Transformers
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What do we know?
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Hans Christian Oersted showed that moving
charges create a magnetic field.
Faraday’s Hypothesis
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If moving charges produced a
magnetic field, could a moving or
changing magnetic field produce a
current?
Faraday’s Discovery
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Faraday discovered that he could induce
current by moving a wire loop through a
magnetic field or moving the magnetic field
through a wire loop.
Faraday’s Discovery is known as
Electromagnetic Induction
Faraday's Discovery
Electromotive Force
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Last week we learned the Lorentz Force.
FB = qvB sinθ = ILB
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When a conductor moves through a magnetic
field, a force is exerted on these charges causing
them to separate, inducing an EMF.
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Electromotive Force
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We know: W = Fd and V = W/q.
V = Fd/q
Using algebra and solving for F:
F = Vq/d
F = qvB
Set these two relationships equal to one another and then
solve for V, which will now be represented as EMF:
EMF (V) = vBL
Where: L is the length of a conductor passing through a
magnetic field.
EMF = Electromotive Force (Volts)
Electromotive Force
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The EMF results when the conductor has a velocity
component perpendicular to the magnetic field.
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Use RHR #1 where the thumb points in the direction of the
velocity. The force on the bar is opposite the velocity.
Example 1: EM Induction
A segment of a wire loop is moving downward
through the poles of a magnet, as shown. What
is the direction of the induced current?
a. The current direction is out-of the page to the left.
b. There is no induced current.
c. The current direction is into the page to the right.
Example 2: EM Induction
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The drawing shows three identical rods (A, B, and C)
moving in different planes in a constant magnetic field
directed along the +y axis. The length of each rod and the
speeds are the same, vA = vB = vC. Which end (1 or 2) of
each rod is positive?
Rod A:
a. 1
b. 2
c. neither
b. 2
c. neither
b. 2
c. neither
Rod B:
a. 1
Rod C:
a. 1
Electromagnetic Induction
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Why is it important?
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Motors
Generators
Transformers
Electric Generators
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Invented by Michael Faraday.
Convert mechanical energy into electrical
energy.
Similar to an electric motor, but function in an
opposite manner.
Electrical power generation is the foundation by
which electricity is supplied to homes and
businesses around the world.
Electricity is generated in many ways hydroelectric, nuclear, coal, gas, oil fired, wind
solar, geothermal.
Magnetic Flux
What is magnetic flux?
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Like electric flux
A measure of the strength of the magnetic field, B,
passing through a surface perpendicular to the field.
For a bar magnet, the flux is maximum at the poles.
The more magnetic field lines, the higher the flux.
=BAcos
Magnetic Flux and EMF
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We already know:
EMF = vBL
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v = Δx/Δt = (x – xo)
(t – to)
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EMF = (Δx/Δt)BL = (xL – xoL) B = (BA) – (BAo)
(t – to)
(t – to)
EMF = -ΔΦ/Δt Where:
Φ = BA cos and
 = the angle the normal
to the surface makes
with B (in this drawing it
is 0o).
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Faraday’s Law of EM Induction
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In the drawing on the previous slide, there is
only one loop in the circuit.
When there is more than one loop in a circuit, as
in the coil of a solenoid, the EMF induced by a
changing magnetic field will increase by a factor
equal to the number of loops in the coil.
EMF = -N ΔΦ/Δt
Where N = the number of loops in the coil.

Note: The units for Φ are Webers (Wb) or 1 Tm2
Magnetic Flux & Generators
Direction of Rotation
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Zero Current
Min Change in Flux
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Max Current
Max Change in Flux Axis of Rotation
Magnetic Flux & Generators
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When the armature is at 90o with the magnetic
field, the current will be zero because the rate of
change in magnetic flux through the coil will be
at a minimum.
When the windings of the armature are aligned
with the direction of the magnetic field, the
current will be at a maximum because the rate
of change in magnetic flux will be at a
maximum.
Principle Operation and
Characteristics of a Generator
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The armature turns such that the coils of wire
cut through the magnetic field inducing an EMF
in the coil.
The magnetic field or the conductor need to be
moving in order for an EMF to be generated.
The greater the change in magnetic field, the
greater the EMF, ie. the faster the armature
turns, the greater the power produced.
Use RHR #1 to determine the direction of
current through the coil.
Generator
Lenz’s Law
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The induced EMF resulting from a changing
magnetic flux has a polarity that leads to an
induced current whose direction is such that
the induced magnetic field opposes the original
flux change.
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If the magnetic field is increasing, a current will
develop to oppose the increasing magnetic field.
If the magnetic field is decreasing, a current will
develop to create a magnetic field in the same
direction as the one that is decreasing.
A current will form that attempts to keep the
magnetic field constant.
Lenz’s Law abides by the laws of conservation of
energy.
Lenz’s Law
Lenz's Law
Lenz’s Law
Current will be
induced in the
copper ring when
it passes through
a region where
the magnetic field
changes. When
the magnetic field
is constant or
absent, there will
be no induced
current.
No Current
Induced
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Applications of Lenz’s Law
(Eddy Currents)
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Eddy current balances.
Eddy current dynamometer.
Metal detectors (Lenz's Law)
Braking systems on trains.
What are Eddy currents?
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Eddy currents are currents created in conductors to
oppose the changing magnetic fields they are exposed
to.
Eddy currents respond to the changes in an external
magnetic field.
Eddy currents can form in conductors even if they are
not capable of being magnetized.
Lenz’s Law and Motors – Back
EMF
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When a current carrying wire moves in a
magnetic field, an EMF is produced called the
back EMF.
The back EMF opposes the current in the motor
resulting in a decrease in the total current
through the motor.
As the motor slows down, the current will
increase.
Back EMF’s may cause sparks at outlets and
switches when circuits are disconnected while in
use.
Back EMF in Electric Motors
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Both motors and generators consist of
coils that rotate in a magnetic field.
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There are two sources of EMF:
• An applied EMF to drive the motor.
• An EMF induced (back EMF) by the generator like
action of the coil that opposes the applied EMF.
EMFnet = Vapplied – EMFinduced
I = (Vapplied – EMFinduced)/R
Self-Inductance
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An increasing current in a coil will induce an EMF
that is opposing to the current in the coil.
NΦ = LI
Where L is a constant called self-inductance.
Substituting into Faraday’s Law of induction:
EMF = -L ΔI/Δt
Note: the negative sign shows that the EMF is
always opposing the change in current.
Note: the faster the change in current, the
greater the EMF.
Transformers
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Transformers are used to
increase or decrease AC
voltage.
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Transformers that increase
voltage are called step-up
transformers.
Transformers that decrease
voltage are called step-down
transformers.
Transformers efficiently
change voltages with little
loss of energy.
Transformer Design
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Transformers consist of
two windings wrapped
around an iron core.
The iron core is easily
magnetized and will
enhance the magnetic
field.
Mutual Inductance: The
changing current in one
coil (primary) will induce
an EMF in the other coil
(secondary).
Transformers (cont.)
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The EMF induced (secondary voltage, Vs) in a secondary
coil is proportional to the primary voltage (Vp).
The EMF induced is also proportional to the number of
windings (Ns) in the secondary coil.
The EMF is inversely proportional to the number of
windings in the primary coil (Np).
Vs/Vp = Ns/Np
Pp = Ps
VpIp = VsIs
Rearranging:
Is/Ip = Vp/Vs = Np/Ns
Power losses are
minimal for
transformers
Key Ideas
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Electromagnetic induction: is the process by
which current is generated by moving a
conductor through a magnetic field or a
magnetic field through a conductor.
The induced current is maximum when the
relative motion of the conductor is perpendicular
to the magnetic field.
The induced voltage is called EMF (=vBL).
Magnetic flux is a measure of the strength of the
magnetic field passing through a surface.
A generator is a device that converts mechanical
energy into electrical energy.
Generators are similar to motors.
Key Ideas
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Lenz’s Law: The induced EMF resulting from a
changing magnetic flux has a polarity that leads
to an induced current whose direction is such
that the induced magnetic field opposes the
original flux change.
Self-Inductance: A changing current in a coil will
induce an EMF that opposes the change in
current.
Transformers convert high voltage/low current
electrical energy to low voltage/high current
electrical energy.
Transformers consist of two coils (primary and
secondary) wrapped around a common iron
core.