21 electromagnetic induction. induction experimental

21 Electromagnetic Induction

Induction Experimental

Magnetic Flux

cosABB

Units: Weber (Wb) 1 Wb = 1T.m2

Faraday’s Law of InductionThe magnitude of the induced emf in a circuit equals the absolute value of the time rate of change of the magnetic flux through the circuit:

tB

for 1 turn or

for N turnst

N B

Generator

tBABAB coscos tAt

B sin

Lenz’s Law: Against the change

The direction of the any magnetically induced current or emf is such as to oppose the direction of the phenomenon causing it.

Lenz’s Law: Example

Motional Electromotive Force

Blvt

tBLv

B

B

“-”sign: Lenz’s LawRecall Lorentz force on the moving part

I ?

Eddy’s Currents

Application: Damping

Application: Speedometer

Application: Hybrid Generator Brake

Mutual Inductance

t

iM

tN

iMNiN

tN

B

BB

B

121

222

12122122

222

or

t

iM

tN B

2

122

111

Similarly,

Define mutual inductance, M,

and t

iM

t

iM

i

N

i

NMMM BB

21

12

2

11

1

222112

Self-Inductance

INL

t

IL

tN

B

B

Unit 1V.s/A = 1 Henry (H)

Examples: Solenoid and Toroid

Transformers

2121

1

222211

1

2

1

2

2211

)/(

/

NN

RR

I

V

RVIVIVI

N

N

tN

tN

eff

BB

and

For an ideal transformer

Transformer & Eddy Current

Magnetic Field Energy

Energy per unit volume (using solenoid)

0

2

2

2

2

1

B

u

LIU

ILItPU

It

ILVIP

B

R-L Circuit  

time

/1)( teR

tI

= L/R, time constant

L-C Circuit

Summary: Electromagnetic Induction & Faraday’s Law

Summary: Lenz’s Law

Summary: Motional EMF

Summary: Eddy’s Currents

Summary: Inductance

Summary: Transformers

Summary: Magnetic Energy

0

2

2

2

2

1

B

u

LIU

ILItPU

It

ILVIP

B

Summary: R-L & R-C Circuits

HomeworkCh21: 1, 4, 12, 16, 21, 25, 27, 32, 40, 45, 52.

P9-Faraday’s Law

P16&17 Lenz’s law

P21&25-Motional emf

P27-Mutual Inductance

2

11

1

22

i

N

i

NM BB

P32-Self-Inductance

INL

t

IL

tN

B

B

P40-Transformer

212

1

2

1

2

)/( NN

RR

N

N

V

V

eff

P45-Magnetic Energy

Voltmeter Construction

d’

V’

gssg

sgsgg

RKd

VRRRkdV

RRKdRRIV

'

')(''

)()(

or

If the V-meter required for maximum V’ (full scale) then

Ammeter Construction

d’

Ig

mcm

cm

divdivA

divdivA

or

or

5.2~10721

101.8

537.0~50101.075.0

8050101.0

'

'

'

6

24

3

3

max

max

-shsh

g

sh

ggshshshgg

shshg

.

RARLength

AKdI

RKd

I

RIRRIRI

IKdIIII