16.360 lecture 23 today dynamic filed faraday’s law stationary loop in a time-varying magnetic...

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16.360 Lecture 23 Today • Dynamic Filed • Faraday’s Law • Stationary loop in a time-varying Magnetic field

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Page 1: 16.360 Lecture 23 Today Dynamic Filed Faraday’s Law Stationary loop in a time-varying Magnetic field

16.360 Lecture 23

Today

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

Page 2: 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

Page 3: 16.360 Lecture 23 Today Dynamic Filed Faraday’s Law Stationary loop in a time-varying Magnetic field

16.360 Lecture 23

Faraday’s Law

, s

sdB

,,t

sdBt

sdt

BldE

s

sC

Page 4: 16.360 Lecture 23 Today Dynamic Filed Faraday’s Law Stationary loop in a time-varying Magnetic field

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

Page 5: 16.360 Lecture 23 Today Dynamic Filed Faraday’s Law Stationary loop in a time-varying Magnetic field

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.

Page 6: 16.360 Lecture 23 Today Dynamic Filed Faraday’s Law Stationary loop in a time-varying Magnetic field

16.360 Lecture 23

Example II

,3.0ˆ tzB

Determine the voltage drops across the two resistors