Chapter 22

Electromagnetic Induction

1) Induced emf and induced current

• Changing B-field induces current

• Changing coil area or orientation induces current

• Changing the number of lines of force through loop induces current

• Induced current indicates induced emf and induced electric field

• Changing magnetic field produces electric field

2) Motional emf

a) The principle

• B-field exerts force on moving charges

€

FB = qvB

+v

FB -v

FB

==> free charges separate

EE

€

E =E / L

• separated charges produce electric field and a corresponding potential difference

EE

• E - field exerts force on charges

+

FE -

FE

€

FE = qE

EE

• Charges stop moving when the forces balance:

€

qvB = qE

€

vB =E /L

Induced emf predicted from statics

€

E =vBL

so,

2) Motional emf

b) Application

c) Induced emf from conservation of energy

FA= FB

FB

€

FB = ILB

FA= FB

FB

€

P =ΔW

Δt

Power to push rod at speed v:

€

P =E (vBL)

R

€

F = ILB and I =E /RUsing,

€

=Δ(FA x)

Δt

€

=FΔx

Δt

€

=Fv

FA= FB

FB

Power to push rod at speed v:

€

P =E (vBL)

R

Electrical power consumed:

€

P =E 2

R

So,

€

E =vBL

3) Magnetic flux,

a) Define Flux:- Proportional to the lines of force through a surface

B

Normal

€

∝| B |

Φ∝ A (area)

Φ∝ cosφ

€

=BAcosφ

b) Flux and motional emf

t

€

E =vBL

€

=Δx

ΔtBL

€

=ΔA

ΔtB

€

=ΔΔt

€

E =ΔΔt

4) Lenz’s law

Direction of induced current produces a magnetic field that opposes the change in flux

-flux into loop increases because of v: ΔΔt > 0

- induced current produces flux out of loop (opposite direction)

-Define external flux as positive. Then

€

E =−ΔΔt

-flux into loop decreases because of v: ΔΔt < 0

- induced current produces flux into loop (same direction to oppose the decrease)

-Define external flux as positive. Then induced flux is also positive, so again

€

E =−ΔΔt

v

5) Faraday’s Law

For any changing flux in any loop, the emf induced in the loop is (for N turns)

€

E =−ΔΔt

N

where is the flux through one turn

7) Induction and sound

• Microphone

• Guitar pickup

• Magnetic tape