Unit 5 Day 1 – Faraday`s Law

Unit 5: Electromagnetism
Day 1: Faraday’s Law of Induction
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
• 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
• These experiments led to the development of Faraday’s
theories of Electromagnetic Induction
• Further experiments doing the opposite, yielded similar
• 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
Magnetic Flux
• Out of Faraday’s investigations, the development of the
concept of magnetic flux developed (similar to electric
 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 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
 
• This is Faraday’s Law of Induction
• If more than one loop is in the coil, then the induced
d B
EMF is:
  N
• Note: d B  either dB  A or B  dA
• The induced current in the circuit will therefore be:
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
Given a closed conducting loop
with B-Field flux lines through the
Determine whether the magnetic flux is increasing or
decreasing. This will determine the direction of the
conventional induced current
The induced current produces (or induces) a magnetic
field which opposes the original externally applied
magnetic field direction
Explanation of Lenz’s Law
Use the RHR to determine the direction of the induced
current & induced EMF from the induced magnetic
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
 1.5V
I 
 .015A (clockwise)
R 100
  N
U  I 2 R  t  (.015A) 2 (100)(0.1s )  .00225J
W U .00225J
 
 .045N