time-varying magnetic fields equation of continuity

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description

time-varying magnetic fields equation of continuity. Faraday 1791-1867. An induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804-65). either B or - PowerPoint PPT Presentation

Transcript of time-varying magnetic fields equation of continuity

An induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804-65).

Faraday’s law dt

tdtV m

ΔsB tΨm

s

dt

tdILtV

zudxdyds

T

BeatV

Tt

2

tTBe

B zu

dt

dtV m

dt

BeadtV

Tt

2

x y

z

dsBm

dsBm

zudxdyds

zuB B

dt

dtV m

dt

tsinABdtV

x y

z

tsinAAs

tcosABtV

x y

z dsBm

dt

dtV m

cosBLWm

dt

d

d

dtV m

tsinBLWtV R

tVtI

dlE

t

dsBdlE

t

dsBdsEdlE

dsEdlE x

Faraday’s law

apply Stoke’s theorem

t

dsB

tx

B

E

tx

dsBdsEdlE

t

x

B

E 0 t

x

B

E 0

0x E

0 B

t

B

tx

B

E

I eat allmagnetic

monopoles!

wire carrying current I

Luwx2

IV o

I

2w

Lu

V

22o

wx

ILwuV

x

Luwx2

Io

Bewley’s book

trick questions not every motion

generates a voltage uniform B & v substitution of circuit Vgen = 0!

XB

XB

1 2

cu

V12= 0

XB

1 2

cu

V12= Bcu

XB

1 2

cu

V12= Bcu

XB

V12= Bcu1 2

cu

XB

1 2

cu

V12= -Bcu

V12= Bcu

XB

1 2

cu

V12= -Bcu

V12= Bcu

1

I1 dl1

B2

I2 dl2

B1

BvdF dQ

dvv BvdF dsdlBjdF

BIdldF

Equation of continuity economics If more comes out

than you put in, the bag will decrease!

There will be a flux of $.

Flux is related to what is or was inside the bag.

note that there is a flux out through a surface z • y @ a time t > 0

[flux density] • s = - [ ($ density)/t] • v evaluate @ xo

t

QI

t

dvv

dsj

t

dvv

dsj

t

dvdv

v

j

t

dvdv

v

j

tv

j

tv

j

Ej

tv

E

tv

E

v

tv

dt

d v

dt

d vv

texpvov

sec10x5.1 19

7

9

10x7.6

10x36

1