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29. Electromagnetic
Induction
1. Induction Experiments
When there is a change in magnetic field, there will be a
momentary current.
 Induced emf
 Induced current
2-3.Faraday’s Law & Lenz’s Law

Magnetic Flux
 B   B  dA

Faraday’s law of induction
dB
E= 
dt
The induced emf in a closed loop equals the negative of the time
rate of change of magnetic flux through the loop
With N turns of wire,
dB
E=  N
dt

Example 29.1) (a) Find the induced emf and the induced current
in the circuit if the loop is a conductor. (b) If the loop is replaced by
one made of an insulator, what effect does this have on the induces
emf and induced current?

Example 29.4) A simple alternator

Example 29.5) A DC generator

Example 29.6) The slidewire generator

Example 29.7) Work and Power in the slidewire generator. Show
that Pdissipated in the circuit is exactly equal to the rate at which work
must be done to move the rod through the magnetic filed.
Resistance of circuit is R.

Lenz’s law
The direction of any magnetic induction effect is such as
to oppose the cause of the effect.
4-5. Motional EMF & Induced Electric
field
dB
E= 
dt
dB
 E  dl   dt

Problem 29.54) The current in the long, straight wire AB is
upward and increasing steadily at a rate di/dt.
a) At an instant when the current is i, what are the magnitude and
direction of the field at a distance r to the right of the wire?
b) What is the flux through the loop?
c) What is the total flux through the loop?
d) What is the induced emf in the loop?
e) Evaluate the numerical value of the induced emf if a=12.0 cm,
b=36.0 cm, L=24.0 cm, and di/dt=9.6A/s.

Displacement Current
q  Cv   0
A
( Ed )   0 EA   0 B
d
dE 

 B  dl  0  iC   0 dt encl  0 (iC  iD )
7. Maxwell’s Equations
 E  dA 
Qencl
0
 B  dA  0
dE 

B

dl


i


0 C
0
  0 (iC  iD )

dt encl

dB
E

dl



dt
dE 

B

dl


i


0 C
0


dt encl

d
1 d
 0iC   0 0  E  dA  0iC  2  E  dA
dt
c dt
dB
d
 E  dl   dt   dt  B  dA

Problem 29.2) A coil with 200 turns enclosing an area of 12 cm2 is
rotated in 0.040 s from a position where its plane is perpendicular to
the earth’s magnetic field to one where its plane is parallel to the
field.
a) What is the total magnetic flux for parallel and perpendicular
position?
b) What is the average induced emf?

Problem 29.10) A circular loop of wire with a radius of 12.0 cm
and oriented in the horizontal xy-plane is located in a region of
uniform magnetic field. A magnetic field with a magnitude of 1.5 T is
directed along the positive z-direction, which is upward.
a) If the loop is removed from the field region in a time interval of
2.010-3 s, find the average emf that will be induced in the wire loop
during the extraction process.
b) If the coil is viewed looking down on it from above, is the induced
current in the loop clockwise or counterclockwise?