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

Moving Loop Example 32-2 Each point on the sides with length a moves in a circle w/ radius b/2 From v = r  = v =  (b/2)  = vB sin  a = ½  Bab sin  Series emf’s add together so:  =  Bab sin  =  ·Area·B·sin  t Recall  =  /t

Alternator Maximum Emf occurs at  t = 1 So, Emf m =  AB Finally  =  m ·sin  t

Alternating current Maximum Emf occurs at  t = 1 So, Emf m =  AB Finally  =  m ·sin  t This changing emf gives us a sinusoidal graph that is periodic Emf (V) Time (s) Side view

Faraday’s Law Using our earlier definition we get Since the current moving clockwise is negative we need to adjust our equation

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 The magnetic flux through the loop When the current changes so does the flux, so the non-electrostatic field is:

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.