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1Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Chapter 20

Lecture

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Chapter 20: Electromagnetic

Induction

Motional EMF

Electric Generators

Faradays Law

Lenzs Law

Transformers

Eddy Currents

Induced Electric Fields

Mutual- and Self-Inductance

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20.1 Motional EMF

Consider a conductor in a B-field moving to the right.

V

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An electron in the conductor

experiences a force downward.

V

e-

F

The electrons in the

bar will move toward

the bottom of the bar.

This creates an electric field in the bar and results in apotential difference between the top and bottom of the bar.

BvF qB

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What if the bar were placed across conducting rails (in red)

so that there is a closed loop for the electrons to follow?

In this circuit, the electrons flow clockwise;

the current is counterclockwise.

VL

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The motional EMF is vBLwhere L is the separation

between the rails.

The current in the rod isR

vBL

RR

VI

where R is the resistance

in the wires.

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The magnitude of the magnetic force on the rod is:

R

LvBLB

R

vBLILBILBF

22

90sin

The rod has a current through it. What is the direction of

the magnetic force on the rod due to the external magnetic

field?

BLF I

Using the right hand rule, the force on the bar is directed

to the left.

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To maintain a constant EMF, the rod must be towed to the

right with constant speed. An external agent must do work

on the bar. (Energy conservation)

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20.2 Electric Generators

A coil of wire is spun in a magnetic field. This produces

an EMF and also a current; both vary with time. (AC-

alternating current)

An energy source is needed to turn the wire coil. Examplesinclude burning coal or natural gas to produce steam; falling

water.

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The EMF produced by an AC generator is:

tt sin0

In the United States and Canada 0 = 170 volts and f =

/2 = 60 Hz.

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20.3 Faradays Law

Moving a conductor through a B-field will generate an EMF.Another way to generate an EMF is to place a stationary

conductor in a B-field that varies with time.

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The magnetic flux is proportional to the number of B-field

lines that cross a given area.

Loop of wire

with area A

cosBAB The unit of magnetic flux is

the weber: 1 Wb = 1 Tm2

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Faradays Law:t

N B

An induced EMF in a coil of N loops is due to a changing

magnetic flux.

Ways to induce an EMF:

1. Vary the magnetic field.

2. Vary the area of the coil.

3. Change the angle between B and A.

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20.4 Lenzs Law

The direction of induced EMFs and currents always oppose

the change in flux that produced them.

That is, the induced I (and thus induced B) tries

to keep the total flux through the loop constant.

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Example: Towing the bar to the right produced an induced

current that was CCW. What is the direction of the induced

magnetic field?

The induced B is out of the page to maintain the flux

originally through the loop before the bar started to move

to the right (the area of the loop is increasing).

VL

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20.6 Transformers

tN B

11

Wrap an iron

core with wire.Primary

coil

Secondary

coil

Apply a varying voltage to the primary coil. This causes a

changing magnetic flux in the secondary coil.

tN B

22

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Since the flux through the coils is the same

2

1

2

1

N

N The turns ratio gives

the ratio of the EMFs.

Depending on the turns ratio, a transformer can be used to

step-up or step-down a voltage.

2

1

1

2

2

1

N

N

I

I

The rate that power is supplied to both coils is the same

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Example (text problem 20.32): A step-down transformer has a

turns ratio of 1/100. An AC voltage of amplitude 170 V is

applied to the primary. If the primary current is 1.0 mA, what

is the secondary current?

A1.0mA0.11

1001

2

1

2

2

1

1

2

IN

NI

N

N

I

I

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Example (text problem 20.34): The primary coil of a

transformer has 250 turns and the secondary coil has 1000

turns. An AC voltage is sent through the primary. The EMF

of the primary is 16.0 V. What is the EMF in the secondary?

V64.0V0.16250

10001

1

2

2

2

1

2

1

N

N

N

N

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20.8 Induced Electric Fields

When a stationary conductor sits in a changing magneticfield it is an induced electric field that causes the charges

in the conductor to move.

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20.9 Mutual- and Self-Inductance

Coil 1

Coil 2

A variable current

I1 flows in coil 1.

I1 then induces a

current in coil 2.

.1212IN The flux (21) through coil 2 due to coil 1 is

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Writing this as an equality,1212

MIN

Where M is the mutual inductance. It depends only on

constants and geometrical factors. The unit of inductance is

the Henry (1H = 1Vs/A).

The induced EMF in the coils will be:

t

IM

tN

t

IM

tN

212

11

121

22

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Self-inductance occurs when a current carrying coil induces

an EMF in itself.

.LIN The definition of self-inductance (L) is

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An inductor stores energy in its magnetic field according to:

2

2

1LIU

The energy density in a magnetic field is:

2

02

1

BuB

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Summary

Motional EMF

Faradays Law

Lenzs Law

Transformers