FARADAY's Law.ppt

7/24/2019 FARADAY's Law.ppt

1/27

Faradays Law

Faradays Law of Induction

Lenzs Law


2/27

Faradays Law of Induction

The emf induced in a circuit is directly proportional

to the time rate of change of the magnetic flux

through the circuit.

dt

d B=E

For N loops,dt

dN

B=E

where,


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4/27

Lenzs LawThe polarity of the induced emf is such that it tends to produce

a current that creates a magnetic flux to oppose the change in

magnetic flux through the area enclosed !y the current loop.

#s the !ar is slid to the right,the flux through the loop

increases.

This induces an emf that will

result in an opposing flux.

$ince the external field is into

the screen, the induced field has

to !e out of the screen.

%hich means a

countercloc&wise current


5/27

Induced EMF


6/27

Determine if the magnetic eld (B) isincreasing

1) 2)


7/27

The area of the coil is increasing.Determine the direction of theinduced current.

3) 4)


8/27

Induced EMF1) 2)


9/27

Induced EMF(change inarea)Increasing #rea of the circle

clockwise


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Induced EMF(change inarea)

clockwise


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Induced EMF (solenoid)


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Induced EMF

# current flows through

the loop when a magnet

is mo"ed near it, without

any !atteries'

The needle deflects

momentarily when the

switch is closed


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Electric uitar

To #mplifier

(ic&up )oil

*agnet

+uitar$tring

N $$N


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END


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Motional EMF

BvF =qB

#s the wire mo"es,

%hich sets the charges in motion in the

direction of Fand lea"es positi"e charges!ehind.

#s they accumulate on the !ottom, an electric

field is set up inside.

In euili!rium,

qEqvB

FFEB

==

vBE=

BlvElV ==


17/27

Motional EMF in a !ircuit

BlxBAB ==

( )dt

dxBlBlx

dt

d

dt

d B ==

=E

Blv=ER

Blv

RI ==

E

If the !ar is mo"ed with constant "elocity,

IlBFF Bapp ==

( )RR

vlBvIlBvFapp

2222E

P ====


18/27

Magnetic Force on a "lidingBar

The !ar has a mass, m, and

an initial "elocity vi

IlBFB =

IlBdt

dvmmaFx ===

R

BlvI=

dtmR

lB

v

dv

vR

lB

dt

dvm

=

=

22

22

122

=

mR

lB

t

ievv =


19/27

Lenzs LawThe polarity of the induced emf is such that it tends to produce

a current that creates a magnetic flux to oppose the change in

magnetic flux through the area enclosed !y the current loop.

#s the !ar is slid to the right,the flux through the loop

increases.

This induces an emf that will

result in an opposing flux.

$ince the external field is into

the screen, the induced field has

to !e out of the screen.

%hich means a

countercloc&wise current


20/27

Energy !onsiderations

$uppose, instead of flowing countercloc&wise, the induced current flows

cloc&wise-

Then the force will !e towards the right

which will accelerate the !ar to the right

which will increase the magnetic flux

which will cause more induced current to flow

which will increase the force on the !ar

and so on

#ll this is inconsistent with the conser"ation of energy


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Mo#ing Magnet and "tationary!oil

/ight mo"ing magnet

increases flux through

the loop. It induces a current that

creates it own magnetic

field to oppose the flux

increase.

Left mo"ing magnet

decreases flux through

the loop. It induces a current that

creates it own magnetic

field to oppose the flux

decrease.


22/27

$%%lication of Lenzs Law

%hen the switch is closed, the flux goes

from zero to a finite "alue in the direction

shown.

To counteract this flux, the induced current in

the ring has to create a field in the opposite

direction.

#fter a few seconds, since there is no change in the flux, no current flows.

%hen the switch is opened again, this time flux decreases, so a current

in the opposite direction will !e induced to counter act this decrease.


23/27

Loo% Mo#ing &hrough aMagnetic Field


24/27

Induced EMF and ElectricFields

)hanging *agnetic Flux 0*F Electric Field Inside aConductor

This induced electric field is non1conser"ati"e and time1"arying

dt

d B

=E

( )rFqW E 2== E

( )rqEq 2=E

rE

2

E=

( )

dtdBrE

Brdt

d

rdt

d

rE B

2

2

1

2

1 2

=

=

=

dt

dd B

= sE.

+eneral Form of

Faradays Law


25/27

Electric Field Induced 'y a !hangingMagnetic Field in a "olenoid

dt

dd B= sE.

( )dt

dBRRB

dt

dd

22. == sE

tItI cos)( max=

( ) dt

dB

RrE

2

2 =

tnItB

nIB

cos)( max0

0

==

( ) tnIRrE sin2 max02=

tr

RnIE

sin

2

2

max0= r2/

2rB

B =

( ) tnIrdt

dBrrE sin2

max0

22 ==

tr

nI

E

sin2

max0

= r3/


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enerators and Motors

tBABAB coscos ==

( )

NAB

tNABtdt

dNAB

dt

dN B

=

==

=

max

sincos

E

E


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Mawells Euations

dt

dd B

= sE.

dt

dId E

+= 000. sB

0. = AB d

0

.

Qd = AE Gauss Law

Gauss Law for Magnetism no magnetic mono!oles

Farada"s Law

#m!$re%Ma&well Law

BvEF += qq Lorent' Force Law

FARADAY's Law.ppt

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