Download L15 Electromagnetic induction and inductance

L15 Electromagnetic induction
and inductance
L15.1 : Electromagnetic induction
Faraday’s law: an electric field is induced (or caused) by a
change of magnetic flux.
Magnetic flux
Lecture outline:
Faraday’s law.
Induced emf.
Lenz’s law.
Electric generators and motors.
Inductance.
Solenoids.
Transformers.
Induced EMF
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L15.2 : Electromagnetic induction
changing flux here
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L15.3 : Electromagnetic induction
An Electromotive Force (EMF) is induced, because of the change
of the magnetic flux.
There are 4 different ways of changing the magnetic flux:
change current here
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move the magnet
If B is uniform,
If there are N loops of wire in a coil:
Total EMF is
stretch the coil
rotate the coil
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L15.4 : Electromagnetic induction
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where B is the flux
through one loop.
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L15.5 : Electromagnetic induction
Consider the rotating loop:
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.”
Flux is
decreasing
Example: eddy currents are produced in conductors that result in
a reduction of the change of magnetic flux.
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.
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!
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charge q
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L15.6 : Electromagnetic induction
Electric generator, dynamo:
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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
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L15.9 : Inductance
The magnetic flux B produced by a current coil is usually
proportional to the current:
where L is the inductance.
(number of turns in coil)
in coil, source EMF = 100V, back EMF = 80V.
Such a coil is called an inductor. The energy in the inductor is
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.
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L15.10 : Inductance
Example: a long solenoid
The magnetic field is
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L15.11 : Inductance
Transformers
A
Consider 2 wires wrapped
around an iron core.
l
and the magnetic flux is
Therefore
Each wire changes contact with
each slip ring half way through each
cycle ("commutator")
DC generator
(car dynamo)
Each wire in contact with
one slip ring.
AC generator
(car alternator)
L15.7 : Electromagnetic induction
AC current (ip) in primary
winding gives alternating
magnetic flux in core, which gives an induced EMF:
&
where
In the secondary winding there is the same flux, so
The energy in the solenoid is therefore
so
the energy per unit volume is
This energy can
be regarded as residing in the magnetic field produced by the coil.
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Therefore
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so we can boost up the voltage by changing
the number of turns.
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L15.12 : Inductance
L15.13 : Inductance
With a load, there is an AC current (is) in the secondary winding.
The power in each winding is
, so
If R is the resistance in the secondary,
So
Contact breaker closed,
current in primary
magnetizes core. Contact
breaker open, collapse of B
gives high induced voltage
in secondary.
which is the effective load seen in the primary winding.
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