Unit 5: Electromagnetism
Day 1: Faraday’s Law of Induction
Objectives:
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•
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•
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Induced EMF
Electromagnetic Induction
Magnetic Flux
Faraday’s law of Induction
Lenz’s Law & it’s Applications
Induced EMF
• Michael Faraday built a circuit that would produce a
current in a secondary winding of a transformer by
allowing a current to flow through the primary winding.
The result was a magnetic field produced in the primary
winding
• The core intensified the magnetic field which produced a
current spike in the secondary winding
• Faraday concluded that the changing magnetic field
through the primary coil is what was responsible for the
current pulse in the secondary
• The current pulse in the secondary coil is called the
induced current
• If the output current fed a load resistor R, then the
induced voltage would be E=IR, called the induced
EMF
• These experiments led to the development of Faraday’s
theories of Electromagnetic Induction
• Further experiments doing the opposite, yielded similar
results
• Moving a magnet through a coil also produces a current
pulse in a wire. Again, Faraday concluded that it was due
to the change in magnetic field that caused the current
pulse
Magnetic Flux
• Out of Faraday’s investigations, the development of the
concept of magnetic flux developed (similar to electric
flux)
 B  B  A  BAcos
for any surface A, made of infinitely small segments dA, of
arbitrary shape:
 B  B   A   B  dA
Magnetic Flux
  B   A   B  dA
B
 B SI units : Tesla  m eter squared (T  m 2 )
1 Tm 2  1 Weber (Wb )
• The number of flux lines per unit area is proportional to
the strength of the magnetic field
• In a loop or coil of wire, the number of B-Field lines
passing through or are enclosed by the loop, is the
magnetic flux
Faraday’s Law of Induction
• Faraday identified that it was the change in the magnetic
field in a coil, that induced an EMF in the circuit (coil)
d B
 
dt
• This is Faraday’s Law of Induction
• If more than one loop is in the coil, then the induced
d B
EMF is:
  N
dt
• Note: d B  either dB  A or B  dA
• The induced current in the circuit will therefore be:
I

R
where R = the resistance of the coil of wire
Lenz’s Law
• The negative sign in Faraday’s Law in Induction is an
indication of the direction of the induced EMF.
• The current produced by the induced EMF moves in a
direction so that the magnetic field created by the
induced current, opposes the original change in flux
This is Lenz’s Law
Explanation of Lenz’s Law
1.
Given a closed conducting loop
with B-Field flux lines through the
loop
2.
Determine whether the magnetic flux is increasing or
decreasing. This will determine the direction of the
conventional induced current
3.
The induced current produces (or induces) a magnetic
field which opposes the original externally applied
magnetic field direction
Explanation of Lenz’s Law
4.
Use the RHR to determine the direction of the induced
current & induced EMF from the induced magnetic
field
Example: Pulling a Coil Through a Magnetic Field
100 turn square coil
l  .05m
R  100
B  .600T (in the paper)
t  0.1s to reach end of B  Field
 B   B  dA  BA  (.600T )(.05m) 2  .0015Wb @ t  0
 B
(0  .0015W )
 100
 1.50V
t
0.1s
 1.5V
I 
 .015A (clockwise)
R 100
  N
U  I 2 R  t  (.015A) 2 (100)(0.1s )  .00225J
W U .00225J
F
 
 .045N
d
d
.05m