notes for chapter 20

7/25/2019 notes for chapter 20

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2/28

BMoving magnetic fields inducecurrents

B

Change the strength of B:Induced current

Induced EMF!

vB

Chapter 20.1 Induced EMF and magnetic flux

Moving current loop induces currents


3/28

Fig. 20.2

Chapter 20.1 Induced EMF and magnetic flux

SI units: weber (Wb)


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20.2&20.4 Faradays law of induction

Michael Faraday1791-1867

Faradays law:The induced emf, , in a closed wire is

equal to the time rate of change of the

magnetic flux, B.

An induced emf,

, always gives rise to acurrent whose magnetic field opposes the

original change in magnetic flux.

Lenzs law

Faradays Law and Lenzs Law both

state that a loop of wire will want its

magnetic flux to remain constant.


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2. A circular loop with a radius of 0.20 m is placed in a

uniform magnetic field B=0.85 T. The normal to the loop

makes an angle of 30o with the direction of B. The field

increases to 0.95 T what is the change in the magnetic flux

through the loop?

B=0.85T

B=0.95T

30o

Change in flux?

' 'cos ' cosB

B A BA =

2'

' 30oA A R

= =

= =

2

2

2

cos ( ' ) cos30( ' )

(0.2) cos30(0.95 0.85)

1.1 10

B

B

B

A B B R B B

x Wb

= =

=

=


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8. A circular coil with a radius of 20 cm is in a field of 0.2 T

with the plane of the coil perpendicular to the field. If the

coil is pulled out of the field in 0.30 s find the average

emf during this interval

B

cos 0B BAN Nt t

= =

2 2

2

0.2 (0.2)

0.3

8.4 10

B R

t

x V

= =

=

N=

cos=A=

1

1R2

B=0


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20.3 Motional emf

x x x x x

x x x x x

x x x x x

x x x x x

A voltage is produced by a conductor moving ina magnetic field

B into the page

v

Charges in the conductor

experience a force upward

F

L

The work done in moving

a charge from bottom to

top

W FL qvBL= =

F qvB=

The potential difference is

WV vBL

q = =

V


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x x x x x

x x x x x

x x x x x

x x x x x

A voltage is produced by a conductor moving in

a magnetic field

B into the page

v

Charges in the conductorexperience a force upward

F

L W FL qvBL= =

F qvB=

The potential difference is

W

V vBLq = =

V

V

olt

a

g

e

velocity

20.3 Motional emf


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20.3 Motional emf

x x x x x

x x x x x

x x x x x

x x x x x

B into the page

vF

L

V

The potential difference can drive a current through a circuit

The emf arises from changing flux due to changing areaaccording to Faradays Law

wire

R

I

Bx AB

V vLB LBt t t

= = = = =

BLvIR R

= =

Changing Magnetic Flux


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x x x x x

x x x x x

x x x x x

x x x x x

B into the page

vF

L

V

18. R= 6.0 and L=1.2 m and B=2.5 T. a) What

speed should the bar be moving to generate a currentof 0.50A in the resistor? b) How much power is

dissipated in R? c) Where does the power come from?

wire

R

I 0.5(6.0)

2.5(1.2)

1.0 /

BLvIR R

IRv

BL

v m s

= =

= =

=

a)

b) 2 2(0.5) (6.0)

1.5

P I R

P W

= =

=

c) Work is done by the

force moving the bar


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Lenzs Law

The polarity of the induced emf is such that it

induces a current whose magnetic field opposes the

change in magnetic flux through the loop. i.e. the

current flows to maintain the original flux through theloop.

NS

V

B Bin

B increasing in loop

Bin acts to oppose thechange in flux

Current direction thatproduces Bin is as

shown (right hand rule)I

+

-

Emf has the polarity shown.

drives current inexternal circuit.

20.4 Lenzs law revisited


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Now reverse the motion of the magnet

NS

V

B

Bin

B decreasing in loop

Bin acts to oppose the

change in flux

Current direction that

produces Bin is as

shown (right hand rule)I

+

-

Emf has the polarity shown.

The current reverses direction



13/28

N S

Lenzs Law and Reaction Forces

NS

V

B Bin

I

A force is exerted by the

magnet on loop to produce thecurrent

A force must be exerted by

the current on the magnet tooppose the change

The current flowing in the direction shown

induces a magnetic dipole in the current loop

that creates a force in the opposite direction

FmcFcm



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B

The flux through the loop

cosB BA =t =

= angular velocity (radians/s)

Normal to the plane

Flux through a rotating loop in a B field20.5 Generators


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B

t

t

B

t

B

t

sinB

BA tt

=

cosB

BA t =

BA

-BA

BA

-BA

BRelation between

Band

proportional to

20.5 Generators


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The emf generated by a loop of N turns rotating at constantangular velocity is

sinNBA t =

t

NBA

-NBA

0

BN

t

=

20.5 Generators


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35. In a model ac generator, a 500 turn rectangular coil

8.0 cmx 20 cm rotates at 120 rev/min in a uniform magnetic

field of 0.60 T. a) What is the maximum emf induced in the

coil?

sinNBA t =

The maximum value of

max

max

(120 2 )

(500)(0.6)(0.08 0.2) 6060

NBA

x

x V

=

= =

20.5 Generators


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Direct Current (DC) generator

20.5 Generators


20/28

DC motor

drives rotation

A generator is motor acting in reverse

I

20.5 Generators


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20.6 Self-Inductance

a property of a circuit carrying a current

a voltage is induced that opposes the change in current

used to make devices called inductors

Self- inductance of a circuit a reverse emf is produce

by the changing current

B

t =


22/28

Self-inductance of a coil

I

Current

increasing

B

B increases,

changes magnetic flux in

the coil,

B A B

t t

=

B

t

Produces emf in coil

B A BN Nt t

= =

The direction of the induced emf opposes the change in

current.

+ -



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InductanceL

is a measure of theself-induced emf

I

Current

increasing

BN

t

=

I

L t

=

The self-induced emf is

L is a property of the coil, Units of L , Henry (H)Vs

A

proportionality constant is L

but B I

t t



25/28

Inductance of a solenoid with N turns and length ,

wound around an air core (assume the length is much

larger than the diameter).

2

o

NL A=

l

B o

NBA IA = =l

B

o

N IA

t t

=

l

2

Bo

N I IN A L

t t t

= = =

l

l

A

I

t

B

t

inductance proportional to N squared x area/length



26/28

An air wound solenoid of 100 turns has a length of 10 cm

and a diameter of 1 cm. Find the inductance of the coil.

2 2 2

7 2 25

4

4 10 (100) (0.01)1.0 10

0.1(4)

o o

N N dL A

L x H

= =

= =

l l

I

l= 10 cm

d=1 cm



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20.7 RL circuits

The inductor prevents therapid buildup of current

But at long time does notreduce the current,

IL

t

=

0I

t

=

at t=

t

oI I (1 e )

=

L

R

=

Applications of Inductors:Reduce rapid changes of

current in circuits

Produce high voltages in

automobile ignition.

f


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20.8 Energy stored in a magnetic field

Energy is stored in a magnetic field of an inductor.

I I=Io

B=0 BoB increasing

Work is done against to produce the B field.

This produces a change in the PE of the inductor

21

2L

PE LI=

This stored PE can be used to do work

notes for chapter 20

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