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Induction
Mr. B
Motional electromotive force
• The movement of a
conductor through a
magnetic to produce
a current
• Example 32-1
• If v is not
perpendicular to B
then the last equation
holds true
Vab  El  vBl
  vBl
Vab  IR    Ir
I

Rr
  v sin Bl
Moving Loop
• Example 32-2
• Each point on the sides with length a
moves in a circle w/ radius b/2
• From v = rw = v = w (b/2)
•  = vB sinq a = ½ wBab sinq
• Series emf’s add together so:
•  = wBab sinq = w·Area·B·sin wt
• Recall w = q/t
Alternator
• Maximum Emf occurs at wt = 1
• So, Emfm = wAB
• Finally  = m·sin wt
Alternating current
Maximum Emf occurs at wt = 1
So, Emfm = wAB
Finally  = m·sin wt
This changing emf gives us a sinusoidal graph that is
periodic
Side view
Emf (V)
•
•
•
•
Time (s)
Faraday’s Law
  BA  Bl s
• Using our earlier definition we get
 Bl s

 vBl
t
t
• Since the current moving clockwise is
negative we need to adjust our equation

 
t
Implications of Faraday
• We can use any changing magnetic field
to produce electricity
• When we change the direction of the
magnetic field we also change the
direction of the current
• So it is either positive (decreasing
magnetic field) or negative (increasing
magnetic field)
• Example 32-4
Induced electric fields
  BA   0 nIA
• The magnetic flux through the loop

I
 
   0 nA
t
t
• When the current changes so does the
flux, so the non-electrostatic field is:
 0 nA I

En 

2r
2r t
Lenz’s Law
• When an emf is generated by a change in
magnetic flux according to Faraday's Law, the
polarity of the induced emf is such that it
produces a current whose magnetic field
opposes the change which produces it.
• The induced magnetic field inside any loop of
wire always acts to keep the magnetic flux in the
loop constant.
• In these examples, if the B field is increasing,
the induced field acts in opposition to it. If it is
decreasing, the induced field acts in the
direction of the applied field to try to keep it
constant.