16.360 lecture 19 exam ii average: 77.8. 16.360 lecture 19 today brief review of electrostatics (i)...

16.360 Lecture 19

• Exam II

Average: 77.8

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16.360 Lecture 19

• Today

Brief review of Electrostatics (I)

1. Maxwell equations2. Charge and current distributions 3. Coulomb’s law4. Gauss’s law5. Electrical scalar potential6. Electrical properties of Materials

16.360 Lecture 19

Maxwell equations

,vD

,t

BE

,0 B

,t

DJH

,ED

,HB

: electrical permittivity; :magnetic permativity

v: electric charge density per unit volume; J: current density per unit area.

,vD

,0 E

,0 B

,JH

Electrostatics Magnetostatics

E: electric field intensity

D: electric flux intensity

H: magnetic field intensity

B: magnetic flux intensity

16.360 Lecture 19

,vD

,0 E

Electrostatics

Volume charge density

,lim0 dv

dq

v

qv

v

Surface charge density

,lim0 ds

dq

s

qs

s

Line charge density

,lim0 dl

dq

l

ql

l

,dvQv v

16.360 Lecture 19

,tsuq v

,sut

qI v

Current density J

,uJ v

,sdJIs

16.360 Lecture 19

,4 2R

qRE

,'EqF

Coulomb’s law

,4

)(3

1

111

RR

RRqE

,

4

)(3

2

222

RR

RRqE

],)()(

[4

13

2

223

1

1121

RR

RRq

RR

RRqEEE

,)(

4

1

13

1

N

ii

i

RR

RRqE

16.360 Lecture 19

Electric field due to a charge distribution

,'4

'ˆ2R

dqREd

,'

'ˆ4

1' 2 v

v

R

dvREdE

,'

''ˆ

4

12

s

s

R

dsREdE

,'

''ˆ

4

12

l

l

R

dlREdE

16.360 Lecture 19

Gauss’s law

,vD

,QdvdvDv vv

, sv

sdDdvD

,QsdDs

Gauss’s law

16.360 Lecture 19

Electrical scalar potential

,ldEdV

,ldEqldFdW e

,qdVdW

,2

1

2

11221

P

P

P

PldEdVVVV

,00 CCldEdV

,0)( CsldEsdE

16.360 Lecture 19

Electrical potential due to point charge

,''4

1)(

'

' dvRR

RVv

v

,4 2R

qRE

,4

ˆ4

ˆ2 R

qdRR

R

qRldEVRR

R

ldEV

Electrical potential due to continuous distributions

,4

)(1RR

qRV

,''4

1)(

'

' dsRR

RVs

s

,''4

1)(

'

' dlRR

RVl

l

16.360 Lecture 19

Electric field as a function of Electrical potential

Poison’s equation

,ldEdV

,ldVdV

,VE

,vD

,vE

,vV ,2

vV Poison’s equation

,02 V Laplace’s equation

16.360 Lecture 19

Electrical properties of material

• conductor• dielectric • semiconductor