9 電磁感應

How did the electric guitar revolutionize

rock?From acoustic to electric

guitars

9-1 Two symmetric Situations

l current loop + magnetic field → torque

l torque + magnetic field → current

9-2 Two ExperimentsFirst ExperimentA Magnet is moving with respect to the loop.

Second Experiment

The switch S is closed or opend.

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 – The magnetic flux

2m1T=1Wb =1Weber A dBB

Electromotive force

Faraday’s law

ε

ε (N turns)

ε

B

B

d

dtd

Ndt

Ε ds

2m1T=1Wb =1Weber A dBB

emf magnetic flux

induced emf

induced electric field

例 1 A solenoid contains a coil

l i =1.5 A ns = 2.2×104

turns / ml A = 3.46 ×10-4m2 Nc = 130 turns

l電流在 25ms內穩定降至 0

計算

mV75/

Wb4.14

T1015.4

,

20

tN

BA

inB

B

iB

i

E

l i =1.5 A n = 2.2×104 turns /

ml A = 3.46 ×10-4m2 N = 130 turns

l電流在 25ms內穩定降至 0

e

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 Movementl Opposition to flux changel Electric Guitars

A6.1

RR

ibatindnet EEE

)10( 2.5

)0.20.8(2

22

tV

tr

dt

dBA

dt

d B

E

例 2 B = 4.0 t2 +2.0 t + 3.0

Ebat = 2.0V r = 0.20m R = 2.0Ω

increasing

clockwise

e

V14144

tdt

d BE

0.3

0

222

22

B

724

4

tdxxHt

HdxxtBHdx

BdAAdB

例 3 B = 4 t2 x2

W = 3.0m H = 2.0m t = 0.1s

increasing

counterclockwisee

9-5 Induction and Energy Transfers

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

RBlvi

BlvdtBldx

dtBlxddtd

BlxBAFvP

/

/

/)(/

,

E

Ee

e

RvLBRRBLvRiP

RvLBFvP

RvLBiLBF

th

m

/)/(

/

/

22222

222

22

The Power

Eddy currents – induction stoves and EM braking

Eddy currents –EM braking

Eddy currents – transformers

Eddy currents – metal detectors

The microphone

The tape recorder

Speaker

Voice-coil positioner of a HDD

9-6 Inductors and Inductance

Inductance:

: flux linkageN

L Ni

1 henry=1H= 1T‧ m2/A

Inductance of a solenoid:

AnlL

lAniBAnliNL

inBBAnlN

20

20

0

/

/))((/

),)((

Inductance of a toroid

a

biNh

r

driNhr

iNr

iNB

ln2

=2

=

hdr2

Bhdr=

AdB= ,2

0b

a

0

b

a

0b

a

0

mHa

bhN

a

biNh

i

N

i

NL 5.2 ln

2ln

2

200

9-7 Self-Induction• An induced emf appears in

any coil in which the current is changing.

dt

diL

dt

NdLiN

)( , E

9-8 Mutual Induction

12212

121

21

212

121212121

1

21221

, ,

, ,

MMdt

diM

dt

diM

dt

dN

dt

diMNiM

i

NM

EE

Two circular close-packed coils

mH3.2

2

2

))((

2

2

121

1

22210

1

212

1

122210

2212212

1

1101

i

NM

R

RNN

i

NM

R

iRNN

RBNN

R

NiB