16.360 lecture 19 exam ii average: 77.8. 16.360 lecture 19 today brief review of electrostatics (i)...
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![Page 1: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/1.jpg)
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
![Page 3: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/3.jpg)
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
![Page 4: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/4.jpg)
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
![Page 5: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/5.jpg)
16.360 Lecture 19
,tsuq v
,sut
qI v
Current density J
,uJ v
,sdJIs
![Page 6: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/6.jpg)
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
![Page 7: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/7.jpg)
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
![Page 8: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/8.jpg)
16.360 Lecture 19
Gauss’s law
,vD
,QdvdvDv vv
, sv
sdDdvD
,QsdDs
Gauss’s law
![Page 9: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/9.jpg)
16.360 Lecture 19
Electrical scalar potential
,ldEdV
,ldEqldFdW e
,qdVdW
,2
1
2
11221
P
P
P
PldEdVVVV
,00 CCldEdV
,0)( CsldEsdE
![Page 10: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/10.jpg)
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
![Page 11: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/11.jpg)
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
![Page 12: 16.360 Lecture 19 Exam II Average: 77.8. 16.360 Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions](https://reader036.vdocuments.us/reader036/viewer/2022062807/56649d4a5503460f94a27dd8/html5/thumbnails/12.jpg)
16.360 Lecture 19
Electrical properties of material
• conductor• dielectric • semiconductor