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

BlvrR

I

IrIRV

vBl

vBlElV

ab

ab

sin

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, Emfm = AB

• Finally = m·sin t

Alternating current

• Maximum Emf occurs at t = 1• So, Emfm = AB• Finally = m·sin t• This changing emf gives us a sinusoidal graph that is

periodic

Em

f (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

t

vBlt

sBl

t

sBlAB

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:

t

I

r

nA

rE

t

InA

t

nIAAB

n

220

0

0

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.