L15 Electromagnetic
induction
Lecture outline:
• Faraday’s law.
• Induced emf.
• Lenz’s law.
• Electric generators and motors.
School of Physics - N. Cramer and R. McPhedran 2001
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L15.1 Electromagnetic
induction
Faraday’s law: an electric field is induced (or caused) by a
change of magnetic flux.
Magnetic flux
Induced EMF
School of Physics - N. Cramer and R. McPhedran 2001
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L15.2 Electromagnetic
induction
There are 4 different ways of changing the magnetic flux:
change current here
changing flux here
move the magnet
rotate the coil
stretch the coil
School of Physics - N. Cramer and R. McPhedran 2001
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L15.3 Electromagnetic
induction
An Electromotive Force (EMF) is induced, because of the change
of the magnetic flux.
If B is uniform,
If there are N loops of wire in a coil:
Total EMF is
where ΦB is the flux
through one loop.
School of Physics - N. Cramer and R. McPhedran 2001
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L15.4 Electromagnetic
induction
Note the minus sign in Faraday’s law: this leads to Lenz’s law:
“when the EMF is induced, the current produces a magnetic field
to oppose the original change in magnetic flux.”
Example: eddy currents are produced in conductors that result in
a reduction of the change of magnetic flux.
Lenz’s law is equivalent to a statement of the conservation of
energy for induced EMFs: we do work against the force opposing
the change of magnetic flux. Otherwise we’d get a perpetual
motion machine!
School of Physics - N. Cramer and R. McPhedran 2001
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L15.5 Electromagnetic
induction
Consider the rotating loop:
Flux is
decreasing
charge q
velocity of wire down
Now
along the wire.
along the wire, and a
So the force on the charge is
current flows along the wire, which produces a magnetic field B1:
This strengthens the original field, so opposes
the change: also i x B produces a force on
the wire opposing the motion.
School of Physics - N. Cramer and R. McPhedran 2001
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L15.6 Electromagnetic
induction
Electric generator, dynamo:
AC generator
(car alternator)
Each wire in contact with
one slip ring.
School of Physics - N. Cramer and R. McPhedran 2001
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L15.7 Electromagnetic
induction
DC generator
(car dynamo)
Each wire changes contact
with each slip ring half
way through each cycle.
B
t
School of Physics - N. Cramer and R. McPhedran 2001
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L15.8 Electromagnetic
induction
Electric motors: The inverse of generators, current leads to motion.
If the torque is constant, why doesn’t the loop get faster and faster?
The rotating loop produces an induced EMF which opposes the
original current, and the torque is reduced (a back EMF).
So we get a balance between work done and energy dissipated in
the circuit.
Example: R = 100 Ω in coil, source EMF = 100V,
back EMF = 80V.
At first, the coil has no rotation, so no change of flux, and
no back EMF. Maximum current, i = 100/100 = 1A.
Finally, coil has steady rotation, back EMF = 80V, total
EMF = 100-80 = 20V. Final current = 20/100 = 0.2A.
School of Physics - N. Cramer and R. McPhedran 2001
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