electromagnetic induction and motionael emf

8/9/2019 electromagnetic induction and motionael emf

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Faradays Law and Inductance

v

B in

F B

F I G U R E 8 . 1 A straight electrical conductor of length, moving with a velocity through a uniform magneticeld directed perpendi-cular to . A current isinduced in the conductordue to the magnetic force oncharged particles in theconductor.

v:B:

v:

Chapter 8


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Figure 8.3

Faradays experiment. When the switch in theprimary circuit is closed, the ammeter needlein the secondary circuit deects momentarily.The emf induced in the secondary circuit iscaused by the changing magnetic eld throughthe secondary coil.

Ammeter

Ammeter

Ammeter

(b)

(a)

N S

(c)

N S

N S

I

I

Figure 8.2

(a) When a magnet is moved towarda loop of wire connected to asensitive ammeter, the amm- eterneedle deects as shown, indicatingthat a current is induced in the

loop. (b) When the magnet is heldstationary, no current is induced inthe loop, even when the magnet isinside the loop. (c) When themagnet is moved away from theloop, the ammeter needle deectsin the opposite direction, indicatingthat the induced current is oppositethat shown in (a).

Ammeter

Secondary coil

Primary coil

Iron

Switch

+

Batter


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B

d A

F I G U R E 8 . 4 The magneticux through an area element is given by .

Note that vector isperpendicular to the surface.d A

:

B:

d A :

B dA cos

d A :


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Loop of area A

B

F I G U R E 8 . 5 A conductingloop that encloses an area

A in the presence of auniform magnetic eld .The angle between andthe normal to the loop is .

B:

B:

(a)

Magnetizedportion of

string

Guitar string

To amplifier

N S

SN

Magnet Pickup

coil

(b)

F I G U R E 8 . 6 (a) In anelectric guitar, a vibratingmagnetized string inducesan emf in a pickup coil(b) The pickups (the circlesbeneath the metallic strings)of this electric guitar detect the vibrations of the stringsand send this informationthrough an amplier andinto speakers. (A switch onthe guitar allows themusician to select which set of six pickups is used.)

( C h a r l e s

D . W

i n t e r s

)


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breaker

coil

current

ring1

2

F I G U R E 8 . 7 (Thinking Physics8.1) Essential components of aground fault interrupter.


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t

B

B max

F I G U R E 8 . 8 (Example 8.2)Exponential decrease in the

magnitude of the magnetic eld with time. The induced emf andinduced current vary with time in

the same way.

B in++

F


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R

B v =

I

R F B

(a)

x

F app

v

B in

I


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B i

B in

I

R

x

y

F v

F I G U R E 8 . 1 2 (Example 8.4) A conducting bar of length,sliding on two xed conductingrails is given an initial velocity in the positive x direction.

v :

i


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(a)

Slip rings N

Brushes

Externalcircuit

Loop

S

t

(b)

max

Externalrotator

Figure 8.13

(a) Schematic diagram of an AC generator. An emf is induced in a loop that rotates in a magnetic eld. (b) A graphical repres- entation of the alternating emf induced in the loop as a function of time.


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Soft ironS

R

Secondary (output)

Primary (input)

V 1

N 1

N 2

F I G U R E 8 . 1 4 (Thinking Physics8.2) An ideal transformerconsists of two coils of wire

wound on the same iron core. Analternating voltage V 1 is appliedto the primary coil, and theoutput voltage V 2 appearsacross the resistance R .


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B in

I

R

(a)

I

R

(b)

v

v


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N S

I

(b)

I

v

(a)

NS

(d)(c)

I

v

S N

I

NS

F I G U R E 8 . 1 6 (a) When the magnet is movedtoward the stationary conducting loop, a current is induced in the direction shown. (b) Thisinduced current produces its own magnetic eldthat is directed to the left within the loop tocounteract the increasing external ux. (c) Whenthe magnet is moved away from the stationary conducting loop, a current is induced in thedirection shown. (d) This induced current produces its own magnetic eld that is directed to

the right within the loop to counteract thedecreasing external ux.

(c)

(a) (b)

Switch

F I G U R E 8 . 1 7 (Example 8.5) A current in the ring is induced when the switch isopened or closed.


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E

E

E

in

r

B

E

F I G U R E 8 . 1 8 A conducting loop of radius rin a uniform magnetic eldperpendicular to the planeof the loop. If changes intime, an electric eld is

induced in a directiontangent to the loop.

B:


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Path of integration

R

r

I max cos t

F I G U R E 8 . 1 9 (Example8.6) A long solenoidcarrying a time-varying

current given by I I

maxcos t . An electric eld isinduced both inside and

outside the solenoid.


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B

R

SI

I

F I G U R E 8 . 2 0 After theswitch is closed, the current

produces a magnetic uxthrough the area enclosedby the loop of the circuit.

As the current increasestoward its nal value, thismagnetic ux changes with

time and induces an emf inthe loop.


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b

a

I

R

S

L +

+

Figure 8.21

A series RL circuit. As thecurrent increases toward itsmaximum value, an emf that

opposes the increasing current isinduced in the inductor.


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R

b

Sa

Figure 8.24

An RL circuit. When the switch S is inposition a, the battery is in the circuit.

When the switch is thrown to position b, thebattery is no longer part of the circuit. Theswitch is designed so that it is never open,

which would cause the current to stop.

t =

t

L

t

R

R

R 0.632

I

Figure 8.22

Plot of current versus timefor the RL circuit shown inFigure 8.23. The switch isopen for t 0 and thenclosed at t 0, and thecurrent increases toward its

maximum value /R. Thetime constant is the timeinterval required for I toreach 63.2% of its maximum

value.

dI dt

t

L

F I G U R E 8 . 2 3 Plot of dI/dt versus time for the RLcircuit shown in Figure 8.21.The time rate of change of current is a maximum at t = 0, which is the instant at

which the switch is closed.The rate decreases expon-entially with time as Iincreases toward itsmaximum value.


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I

t

R

Figure 8.25

Current versus time for theright-hand loop of thecircuit shown in Figure 8.26.

F I G U R E 8 . 2 6 (Example 8.8) (a) The switch in this RL circuit is open for t 0 and then closed at t 0.(b) A graph of the current versus time for the circuit in (a).

t (ms)0 2 4 6 8 10

0

1

2

I (A)

(b)(a)

30.0 mH

12.0 V 6.00

S 12 14


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S1

S2

R

L

b

a

(a)

S1

S2

R

L

b

a

(b)

S1

S2

R

L

b

a

(c)

F I G U R E 8 . 2 7 An RL circuit used for conceptualizing energy storage in an inductor. (a) With the switchesas shown, the battery establishes a current through the inductor. (b) Switch S1 is thrown to position b.Because the ends of the inductor are connected by a resistance-free path, the current continues to owthrough the inductor. (c) Switch S2 is opened, adding the resistor to the circuit, and energy is delivered to theresistor. This energy can only have been stored in the inductor because that is the only other element in thecircuit.


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I

b dr

r I

a

B

F I G U R E 8 . 2 8 (Example 8.10) Section of along coaxial cable. The inner and outerconductors carry equal currents in opposite

directions.


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E

B in

+

+

+

v

Figure Q8.3 Questions 8.3 and8.4.

v :

R

S

N

v

Figure Q

8.2

B out

v

Figure Q8.5 Questions 8.5and 8.6.

( C o u r t e s y o

f C E N C O )

(a)

Iron core

Metal ring

S

(b)

Figure Q8.9 Questions 8.9 and 8.10.


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R

S

Figure Q8.11

R

L

Switch

Figure Q8.15

I

r 1


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.

I

w

h

L

Figure P8.4 Problem 8.4

I

15-turn coil

R

Figure P8.5

V 1 V 2

d

v

S N

Figure P8.7


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app

R

F

Figure P8.11 Problems 8.11 ,8.12, 8.13, and 8.14.

B

Figure P8.16


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( R o s s

H a r r

i s o n

/ G e t t y

I m a g e s

)

Figure P8.18

v

R

S N

R

S)b()a(

I

(c)

R

(d)

++

v

Figure P8.19

v

B in


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R AreaA

r

Figure P8.28

L

R

S

Figure P8.31 Problems 8.31 ,8.32 , and 8.34.


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12.0 V 1 200

12.0

2.00 H

Sa

b

Figure P8.36

a b c d e t

F I G U R E 8 . 1 (Quick Quiz 8.2) The timebehavior of a magnetic eld through a loop.


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F I G U R E 8 . 2 (Quick Quiz 8.5) In an old-fashionedequal-arm balance, an aluminum sheet hangs betweenthe poles of a magnet.

( P h o t o s

b y

J o

h n

J e w e t t

)

S

L

Iron bar

F I G U R E 8 .3 (Quick Quiz 8.7) A lightbulb is powered by an AC source

with an inductor in the circuit. When the iron bar is inserted into the coil, what happens to the brightness of the lightbulb?


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B 0

B tot

I

0

I

5 10 15

A

B

t (s)

F I G U R E Q4 (Quick Quiz 8.8) Currenttimegraphs for two circuits with different inductances.

electromagnetic induction and motionael emf

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