Transcript PHY 231 Lecture 29 (Fall 2006)

Physics 213
General Physics
Lecture 12
Last Meeting: Faraday’s Law of
Induction, Lenz’ Law
Today: Finish Faraday’s and Lenz’
Laws, Self Inductance, RL Circuits,
Energy Stored
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
( Blx )
x
 

  Bl
  Blv
t
t
t
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
Demo

Rail and Magnetic Flux
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
Demo

Levitating Floppy Disc in Large Magnet
 Levitating Metal Plate
 Magnets Falling through Copper and Plastic
Tubes
 Eddy Current Pendulum
 Thomson Coil
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AC Generators, cont

Basic operation of the
generator

As the loop rotates, the magnetic
flux through it changes with time
 This induces an emf and a current
in the external circuit
 The ends of the loop are
connected to slip rings that rotate
with the loop
 Connections to the external circuit
are made by stationary brushes in
contact with the slip rings
AC Generators

The emf generated by the
rotating loop can be found by
ε =2 B ℓ v=2 B ℓ sin θ

If the loop rotates with a
constant angular speed, ω,
and N turns
ε = N B A ω sin ω t


ε = εmax when loop is parallel
to the field
ε = 0 when when the loop is
perpendicular to the field
Self-inductance

Self-inductance occurs when the changing
flux through a circuit arises from the circuit
itself

As the current increases, the
magnetic flux through a loop due to
this current also increases
 The increasing flux induces an emf
that opposes the change in
magnetic flux
 As the magnitude of the current
increases, the rate of increase
lessens and the induced emf
decreases
 This opposing emf results in a
gradual increase of the current
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=
<<
19
N B
N
N
B  0 I   B  BA  0 I  r 2
l
l
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Inductor in a Circuit

Inductance can be interpreted as a measure of
opposition to the rate of change in the current
 Remember
resistance R is a measure of opposition to
the current

As a circuit is completed, the current begins to
increase, but the inductor produces an emf that
opposes the increasing current
 Therefore,
the current doesn’t change from 0 to its
maximum instantaneously
RL Circuit


When the current
reaches its maximum,
the rate of change and
the back emf are zero
The time constant, , for
an RL circuit is the time
required for the current
in the circuit to reach
63.2% of its final value
I 

1e


R
t / 