9 電磁感應

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9 電磁感應

How did the electric guitar revolutionize

rock?

From acoustic to electric guitars

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9-1 Two symmetric Situations

l current loop + magnetic field → torque

l torque + magnetic field → current

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9-2 Two Experiments

First Experiment

A Magnet is moving with respect to the loop.

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Second Experiment

The switch S is closed or opend.

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9-3 Faraday’s Law of Induction

l An emf is induced when the number of magnetic field lines that pass

through the loop is changing.

– A Quantitative Treatment

– ^B The magnetic flux



^B^  ^dA^ 1Weber = 1Wb = 1T m²

Electromotive force

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Faraday’s law

ε

ε (N turns)

ε

B

d dt N d

dt Εds

  



 

^  ^

m2

1T

= 1Wb

= 1Weber

A 





^B



^B^ ^d ^

emf magnetic flux

induced emf

induced electric field

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例 1 A solenoid contains a coil

l i =1.5 A n_s = 2.2×10⁴ turns / m

l A = 3.46 ^×10^-4m²N_c = 130 turns

l

電流在 25ms 內穩定降至 0

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計算

mV 75

/

Wb 4

. 14

T 10

15 .

4

,

2 0















 ^

t N

BA in B

B i

E



l i =1.5 A n = 2.2×10⁴turns / m

l A = 3.46 ^×10^-4m²N = 130 turns

l

電流在 25ms 內穩定降至 0

e

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感應電流所生的磁場與感應出該電流的磁場反向

9-4 Lenz’s Law

l Opposition to pole Movement

l Opposition to flux change

l Electric Guitars

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例 2 B = 4.0 t

²

+2.0 t +

Ebat = 2.0V r = 0.20m R = 2.0Ω

3.0

increasing

clockwise

e

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例 3 B = 4 t

²

x

²

W = 3.0m H = 2.0m t

= 0.1s

increasing

counterclockwise

e

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9-5 Induction and Energy Transfers

The work done by the applied force and the thermal energy produced in the wire.

R Blv

i

Blv dt

Bldx

dt Blx

d dt

d

Blx BA

Fv P

/ /

/ ) (

/ ,









 E E^e

e

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R v

L B R

R BLv

R i

P

R v

L B Fv

P

R v

L B iLB

F

th m

/ )

/ (

/ /

2 2 2 2

2

2 2 2

2 2



The Power

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Eddy currents –

induction stoves and

EM braking

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Eddy currents –EM

braking

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Eddy currents –

transformers

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Eddy currents – metal

detectors

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The microphone

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The tape recorder

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Speaker

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Voice-coil

positioner of a

HDD

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9-6 Inductors and

Inductance

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Inductance of a solenoid:

A n

l L

lA n

i BA

nl i

N L

in B

BA nl

N

2 0

0

/

/ ) )(

( /

), )(

(















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Inductance of a toroid

a b iNh

r dr iNh

r iN r

B iN

2 ln 2 =

=

2 hdr Bhdr

=

A d B

= 2 ,

b 0 a 0

b a b 0

a 0







 

















  

a mH b h

N a

b iNh

i N i

L N ln 2.5

ln 2 2

2 0

0  

 

 







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9-7 Self-Induction

• An induced emf appears in

any coil in which the current is changing.

dt L di dt

N Li d

N    (  )  

, E

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9-8 Mutual Induction

12 2 21

1 12 21

2 21 21 1

21 2

1 21 1

21 21 2

,

M dt M

M di dt

M di

dt N d

dt M di

N i

i M M N













 



 



E E

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Two circular close-packed coils

mH 3

. 2

2 2

) )(

( 2

2 12 1

1

2 2 2 1 0 1

21 2

1

1 2 2 2 1 0

2 2 1

2 21

2

1 1 1 1 0

 



 







i M N

R

R N N i

M N

R

i R N N

R B

N N

R N B i







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