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Lesson 9. Lesson 9. Faraday’s Law. Faraday’s Law of Induction Motional EMF Lenz’s Law Induced EMF’s and Induced Electric Fields Eddy Currents. Torque on Loop. Current in loop in a magnetic field produces torque on a loop. Induced Current.

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lesson 9
Lesson 9

Lesson 9

Faraday’s Law

  • Faraday’s Law of Induction
  • Motional EMF
  • Lenz’s Law
  • Induced EMF’s and Induced Electric Fields
  • Eddy Currents
torque on loop
Torque on Loop

Current in loop in a magnetic field produces torque on a loop

induced current
Induced Current

Does torque on loop in a magnetic field produces current in a loop ?

YES

picture
Picture

I

B

  • current depends on the torque
  • thus on rotational frequency
change of flux picture
Change of Flux Picture
  • Current depends on speed of magnet
  • Thus rate of change of magnetic Field
change of flux picture equations
Change of Flux Picture Equations

Common factors, change of area, change of magnetic field

induced current in wire
Induced Current in Wire

moving wire in field B produces current I if there is a conduction path

I

B

v

FB

induced emf
Induced emf

(y,

z1)

(y,

z2)

y1

k

j

i

equations ii
Equations II

Work done per unit charge by

F

B

in moving charges from

z

to

z

1

2

=

vBl

where

l

=

z

-

z

2

1

No work is done in moving charges in

other sections of path

(

ignore Hall effect

)

dW

Work done per unit charge

=

emf

dQ

Thus

e

=

vBl

equations iii
Equations III

Area of loop in magnetic field

(

)

(

)

(

)

A

t

=

y

t

-

y

l

1

Total magnetic flux through loop

(

)

F

t

Rate of change of magnetic flux

e

d

F

dy

=

-B

l

=

-

Bvl

=

-

dt

dt

slide12

Faraday

s Law of Induction for N loops

faradays law of electromagnetic induction

'

Faradays Law of Electromagnetic Induction

The work done per unit charge by magnetic force

moving charge from

z

to

z

1

2

ò

ò

ò

z

2

dW

1

1

=

·

=

·

=

·

F

s

F

s

E

s

d

d

d

B

B

ind

dQ

Q

Q

z

loop

loop

1

thus

ò

e

F

d

=

-

=

·

d

E

s

N

ind

dt

loop

induced electric field
Induced Electric Field
  • An induced EMF is a measure of
  • An induced Electric Field
  • If charge is in this region and there is a conduction path it will feel a force from the induced Electric Field and flow
equations
Equations

E

Remember for a static electric field

stat

ò

b

=

·

E

s

V

d

and

ab

stat

a

ò

=

·

=

E

s

E

d

0

as

is conservative

stat

stat

E

But for an induced electric field

ind

ò

·

¹

E

s

d

0

ind

thus

E

is not conservative

ind

magnetic flux and induced electric field
Magnetic Flux and Induced Electric Field

Changing Magnetic Flux produces an

Induced Electric Field

mechanical work to electrical work i
Mechanical Work to Electrical work I

Pulling at constant velocity v

B

v

l

Fappl

I

Blv

y

k

j

i

mechanical work to electrical work ii
Mechanical Work to Electrical work II

l

wire

with current I flowing in it

B

moving in a magnetic field

feels a force given by

=

´

F

l

B

I

=

-

´

=

-

F

k

i

j

IlB

IlB

F

This force opposes the applied force

appl

and must be equal and opposite if the

velocity is to remain constant

=

=

F

F

IlB

appl

mechanical power to electrical power ii
Mechanical Power to Electrical Power II

Pulling at constant velocity v

B

v

F

l

Fappl

I

Blv

magnetic field produced by changing current
Magnetic Field produced by Changing Current

Circulating current produces an induced magnetic field

I

Bind

That opposes the external magnetic field B

That produces the current

current produced by changing magnetic field
Current produced by Changing Magnetic Field

(a) Change of External Magnetic Field Produces Current

(b) Current Produces Induced Magnetic Field

lenz s law
Lenz's Law

Lenz’s Law

Polarity of is such that

it opposes the change that caused it

Direction of Eis such that

it opposes the change that caused it

Direction of induced current is such that

it opposes the change that caused it

conservation of energy
Conservation of Energy

Conservation of Energy

ac generator
AC Generator

AC Generator

ac potential

e

AC Potential

F

d

d

(

)

(

)

=

-

=

-

·

B

A

t

dt

dt

d

(

)

(

)

=

-

=

q

BACos

BA

sin

d

q

(

t

)

q

t

dt

dt

if rotational speed is constant

e

e

(

)

(

)

(

)

w

w

t

wBA

sin

t

sin

t

=

=

max

e

=

BAw

max

dc generator
DC Generator

DC Generator