16.360 Lecture 23

Today

• Dynamic Filed • Faraday’s Law• Stationary loop in a time-varying Magnetic field

16.360 Lecture 23

Static field

,vD

,0 E

Dynamic Field

,0 B

,JH

,

ˆ

4 2

l R

RldIH

,vD

,t

BE

,0 B

,t

DJH

,'

'ˆ4

1' 2 v

v

R

dvREdE

16.360 Lecture 23

Faraday’s Law

, s

sdB

,,t

sdBt

sdt

BldE

s

sC

16.360 Lecture 23

Electromotive force

,t

sdt

BldEV

sCemf

,memf

tremfemf VVV

Stationary Loop in a Time-varying Magnetic field

,

s

tremf sd

t

BV

,

s

i

tremf sd

t

B

RR

VI

Lenz’s law

16.360 Lecture 23

,)(

ssCemf sdEsd

t

BldEV

An example:

,sin)3ˆ2ˆ(0 tzyBB

Faraday’s law, differential form,t

BE

(a) The magnetic flux link of a single turn of the inductor.

(b) The transformer emf,.

(c) The polarity of the emf.

(d) The induced current.

16.360 Lecture 23

Example II

,3.0ˆ tzB

Determine the voltage drops across the two resistors