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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
