29. Electromagnetic Induction. When there is a change in magnetic field, there will be a momentary current. Induced emf Induced current 1. Induction.

29. Electromagnetic Induction

When there is a change in magnetic field, there will be a momentary current.

Induced emf Induced current

1. Induction Experiments

Magnetic Flux

B B dA

2-3.Faraday’s Law & Lenz’s Law

Faraday’s law of induction

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,

Bd

dt

E=

BdNdt

E=

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

BdE dl

dt

Bd

dt

E=

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

0 0 0( ) B

Aq Cv Ed EA

d

0 0 0 ( )EC C D

encl

dB dl i i i

dt

7. Maxwell’s Equations

0

enclQE dA

0B dA

0 0 0 ( )EC C D

encl

dB dl i i i

dt

Bd

E dldt

0 0

0 0 0 0 2

1

EC

encl

C C

dB dl i

dt

d di E dA i E dA

dt c dt

Bd dE dl B dA

dt dt

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 2.010-3 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?