Section 6 Dielectrics C onstant currents are impossible Constant internal electric fields are possible No macroscopic currents Macroscopic field Might be locally nonzero Neutral dielectric Includes only charges belonging to dielectric namely electrons and protons of neutral constitu ID: 731264
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Slide1
The electric field in dielectrics
Section 6Slide2
Dielectrics:
C
onstant currents are impossibleConstant internal electric fields are possible.
No macroscopic currents
Macroscopic field
Might be locally non-zeroSlide3
Neutral dielectric: Includes only charges belonging to dielectric, namely electrons and protons of neutral constituent atoms
Total charge =
Hence
where
P
= 0 outside the dielectric
Over volume of dielectric
On boundary that surrounds dielectric
since
P
= 0 outside the dielectricProof P is the “dielectric polarization” or “polarization”. If non-zero, body is “polarized”.Slide4
The component of P along the outward normal =
P
n
=
P.n
= sSlide5
Total dipole moment of the dielectric
i
th
component
surface
Sum over j
Dipole moment =
= dipole moment per unit volumeSlide6
Still talking about neutral dielectrics
Holds both inside and outside (where
D
=
E
)
“Electric induction”
Average <
r
>
r is over charges belonging to the dielectricSlide7
If extraneous charges are added, we get a “charged” dielectric
Extraneous charge densitySlide8
Boundary between two
dielectrics
E
1t = E2tTangential component of electric field is continuous
=
E
1
E
2Slide9
Boundary between two dielectrics
D
1
If
D
n
=
D
z
were discontinuous, then
which would contradictSlide10
Boundary between dielectric and conductor
E
t = 0 in the conductor
Curl E = 0 still holdsEt is continuousTherefore Et = 0 on both sidesSlide11
Even a neutral conductor can have surface charge (but no
P
)
Surface charge density on conductor = extraneous charge on dielectric
dielectric
conductorSlide12
Name and unit conventions
Landau, Gaussian Units
D
= E + 4 p P = electric induction
D,E,P all have the same unitsDiv D = 4 p rex
(extraneous charge density)
Div E = 4 p <r>r (total charge density, intrinsic + extraneous)
Other books, S.I. unitsD = e0E + P = electric
displacementD,P have the same units, E has different units (V/m)Div D = rf
(free charge density)Div
E = r/e0 (total charge density, bound+ free)