16.360 Lecture 20

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• Conductors• Resistance• Dielectrics • Electric boundary conditions• Capacitance• Electrostatic potential energy• Image method

16.360 Lecture 20

Conductors

Electron drift velocity Eu ee

Hole drift velocity Eu hh

Conducting current

,)( EuuJJJ hvhevehvhevehe

,hvheve

,EJ

Point form of Ohm’s law

16.360 Lecture 20

Resistance,1

221 lEldEVVV x

x

x

General form

,AEsdEsdJI xAA

,Al

IVR

,

1

2

1

2

A

x

x

A

x

x

sdE

ldE

sdJ

ldE

IVR

16.360 Lecture 20

Joule’s law

,hhee lFlFW

General form

,

)(

vEJ

vEuEuuFuFtlF

tlF

tWP

hvhevehhee

hh

ee

v

dvEJP ,

16.360 Lecture 20

Dielectrics

Electrical field induced polarization

16.360 Lecture 20

Dielectrics

,0 PED

P: electric polarization field

For homogeneous material:

,0 EP e

,000 EEEPED e

),1(0 e

),1(0

er Relative permittivity:

Electric susceptibility

Dielectric breakdown

16.360 Lecture 20

Electric boundary condition

;0][ 120

lim

ldEldEldEd

c

b

ahC

,111 nt EEE

,222 nt EEE

,021 lElE tt

,21 tt EE

the tangential component is continuousacross the boundary of two media.

16.360 Lecture 20

Electric boundary condition

;][lim0

ssdDsdDsdD sbottomtophC

,21 ssDsD snn

the normal component of D changes, theamount of change is equal to the surfaceCharge density.

,21 snn DD

16.360 Lecture 20

Dielectric-Conductor boundary

,1 snD

,021 tt EE

16.360 Lecture 20

Conductor-Conductor boundary

,221121 snnnn EEDD

,21 tt EE

,2

2

1

1

tt JJ

,

2

22

1

11 s

nn JJ

,)(2

2

1

11 snJ

16.360 Lecture 20

Capacitance

, s

sdEQ

,VQC

l

ldEV

,

RC

,

l

s

ldE

sdEC

,

1

2

1

2

A

x

x

A

x

x

sdE

ldE

sdJ

ldE

IVR

16.360 Lecture 20

Electrostatic Potential Energy

,ldWldFdW ee

,

21 EDWe

,eWF

Image Method

Any given charge above an infinite, perfect conducting plane is electrically equivalent to the combination of the give charge and it’s image with conductingplane removed.