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16.360 Lecture 28
Last lecture:
• The electromagnetic generator • Moving conductor in a time varying magnetic field• Displacement current
16.360 Lecture 28
The electromagnetic generator
),cos(
)cos(
00
0
CtAB
ABsdBS
),sin(
)cos(
00
00
CtBA
CtABdt
d
dt
dVemf
16.360 Lecture 28
Moving conductor in a time-varying magnetic field
,)( ldBusdt
BVVVldE
Cs
memf
tremfemfC
Example:
,101 AI ,ˆ5yu
10R
?2 I
16.360 Lecture 28
Displacement current
,JH
• Ampere’s law in static electric field
,t
DJH
• Ampere’s law in time-varying electric field
• proof of Ampere’s law:
,vD
,)( sv
sdDdvDQ
,)()('
ssvS
sdDt
sdDt
dvDt
Qt
sdJI
t
DJ
' Displacement current density
16.360 Lecture 28
Displacement current
,t
DJH
• Ampere’s law in time-varying electric field
Example: ,cos0 tVVs
,sin01 tCVdt
dVCI C
c
,cosˆˆ 0 td
Vy
d
VyE c
,sin02 tCVsdt
DI
Sd
16.360 Lecture 28
Today
• Boundary conditions for Electromagnetic• Charge-current continuity relation• Free charge dissipation in a conductor
16.360 Lecture 28
• Boundary conditions for Electromagnetic
,t
BE
,t
DJH
,0 B
,vD
,21 vnn DD
,21 tt EE
,21 nn BB
,21 stt JHH
Maxwell equations boundary conditions
16.360 Lecture 28
• Charge-Current continuity Relation
charge current continuity equation
,
v vdvt
Qt
I
,
v vsdv
tsdJI
,
v vvsdv
tJsdJ
,vtJ
,0 sdJs
steady state integral form
,0i
iI Kirchhoff’s current law
16.360 Lecture 28
• Free-charge dissipation in a conductor
,vtJ
,EJ
,vtJD
,vv t
,/ rtvov e ,
r