Ch 21 1

Chapter 21

Electromagnetic InductionFaraday’s Law

AC Circuits

© 2006, B.J. LiebSome figures electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey

Giancoli, PHYSICS,6/E © 2004.

Ch 21 2

Induction

•Discovered in 1820 by Michael Faraday and Joseph Henry

•Magnetic field causes a current, but only when the magnetic flux is changing.

Ch 21 3

Magnetic Flux

•Necessary to explain induction

•In the figure below A is the area of a surface-usually the area inside of a coil of wire.

cosBAABB

•In a properly drawn magnetic field, flux is proportional to the total number of lines passing through a point.

Ch 21 4

Faraday’s Law of induction

• the flux B can change because

B is changing

A is changing or moving

A is rotating

tN B

Ch 21 5

Lenz’s LawAn induced emf always gives rise to a current whose magnetic field

opposes the original change in flux. In the figure below:

(a) Original state is no flux, so current flows in clockwise direction which would give a downward magnetic flux

(b) Original state is upward flux so current flows counterclockwise to maintain that state.

(c) No flux change, so no current.

Ch 21 6

Example In the figures below, a circular loop of wire and a straight wire carrying a current lie on the surface of a table. The straight wire is shown as an arrow in the current direction. Determine the direction of the current induced in the loop of wire due to the changing current in the straight wire for each figure.

I increasing

I decreasing

I constant I increasing

Ch 21 7

Example 21-2 The loop shown is a 10-turn coil of wire of radius 12 cm and is in a magnetic field of strength 0.15 T. Calculate the average EMF induced if the coil rotates 900 about an axis perpendicular to the field in 0.20 seconds.

cosABB

0Initially

ABABBi 0cos

90PositionFinal

090cos ABBf

t

N B

t

ABN

0t

ABN

s

mT

20.0

)045.0()15.0(10 2

V34.0

2RA 2)12.0( m

2045.0 m

Ch 21 8

Example 21-1

tB

t

AB

t

xlB

vlB

vlB)4.3()35.0()45.0( smmT

V54.0

RI

RI

23.0

54.0 V A3.2

clockwise

isitsofluxdownwarda

maintaintotriescurrent

wirem0.35theonforce

magneticthefromforcethecalculatecanWe

sinBlIF BlI

BlIF )45.0()35.0()3.2( TmA

NmA

NmA 36.036.0

Ch 21 9

Electric Generators

A coil of wire rotating in a magnetic field experiences an sinusoidal EMF:

sinNBlv2This is the basis of electric generator.

Ch 21 10

Transformers

Changing current in the primary creates a changing flux in the secondary coil

tNV B

ss

t

NV BPP

If the flux change is equal

p

s

p

s

N

N

V

V

In an ideal transformer: Power Out = Power In

sspp IVIV

Ch 21 11

Example 21-3

P

S

P

S

N

N

V

V

PP

SS V

N

NV

V120

330

1240

V45

OUTPOWERINPOWER

sSPP VIVI

SP

SP I

V

VI

A

V

V15

120

451

A56

Ch 21 12

Power Grid

Power is transmitted at the highest possible voltage in order to minimize losses.