16.360 Lecture 20
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Transcript of 16.360 Lecture 20
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16.360 Lecture 20
Today
• Conductors• Resistance• Dielectrics • Electric boundary conditions• Capacitance• Electrostatic potential energy• Image method
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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
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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
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16.360 Lecture 20
Joule’s law
,hhee lFlFW
General form
,
)(
vEJ
vEuEuuFuFtlF
tlF
tWP
hvhevehhee
hh
ee
v
dvEJP ,
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16.360 Lecture 20
Dielectrics
Electrical field induced polarization
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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
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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.
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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
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16.360 Lecture 20
Dielectric-Conductor boundary
,1 snD
,021 tt EE
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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
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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
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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.