The Electric Field in Dielectrics
The electric field in dielectrics
Section 6
1. Dielectrics:
Constant currents are impossible
Constant internal electric fields are possible.
No macroscopic
currents
Macroscopic field
Might be locally non-zero
2. Neutral dielectric: Includes only charges belonging to the 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 dielectric
Proof
P
is the “dielectric polarization” or “polarization”. If non-zero, body is “polarized”.
The component of P along the outward normal = P
n
=
P.n
=
3. The meaning of
P
is found from the total dipole moment of the dielectric
i
th
component
surface
Sum over j
Dipole moment =
= dipole moment per unit volume
4.
Introducing the Electric Induction
Holds both inside and
outside (where
D
=
E
)
“Electric induction”
For neutral dielectrics, average <
>
r
is over charges
belonging
to the dielectric
If extraneous charges are added,
we get a “charged” dielectric
Extraneous charge density
6. Boundary between two dielectrics
E
1t
=
E
2t
Tangential component of electric field is continuous
=
E
1
E
2
Boundary between two neutral dielectrics
D
1
If D
n
= D
z
were discontinuous, then
which would contradict
Boundary between dielectric and conductor
•
E
t
= 0 in the conductor
•
Curl
E
= 0 still holds
•
E
t
is continuous
•
Therefore
E
t
= 0 on both sides
A conductor can have surface charge, which is extraneous to the
dielectric. E and P are both 0 in the conductor, so D = 0 there.
Surface charge density on conductor = extraneous charge on dielectric
dielectric
conductor
Name and unit conventions
•
Landau, Gaussian Units
D
=
E
+ 4
P
= electric
induction
D,E,P all have the same units
Div
D
= 4
ex
(
extraneous
charge density)
Div
E
= 4
<
>
r
(total charge density, intrinsic + extraneous)
•
Other books, S.I. units
D
=
0
E
+
P
= electric
displacement
D,P have the same units, E has different units (V/m)
Div
D
=
f
(
free
charge density)
Div
E
=
/
0
(total charge density, bound+ free)
Dielectrics play a crucial role in the formation of electric fields, with constant internal fields possible but constant currents impossible. The concept of neutrality in dielectrics and the boundary conditions between different materials are explored, shedding light on polarization and electric induction phenomena.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
The electric field in dielectrics Section 6
1. Dielectrics: Constant currents are impossible Constant internal electric fields are possible. No macroscopic currents Macroscopic field Might be locally non-zero
2. Neutral dielectric: Includes only charges belonging to the dielectric, namely electrons and protons of neutral constituent atoms Total charge = where P = 0 outside the dielectric Hence Proof Over volume of dielectric On boundary that surrounds dielectric since P = 0 outside the dielectric Pis the dielectric polarization or polarization . If non-zero, body is polarized .
3. The meaning of P is found from the total dipole moment of the dielectric ith component surface Sum over j Dipole moment = = dipole moment per unit volume
4. Introducing the Electric Induction For neutral dielectrics, average < >r is over charges belonging to the dielectric Holds both inside and outside (where D = E) Electric induction If extraneous charges are added, we get a charged dielectric Extraneous charge density
6. Boundary between two dielectrics E1 = E2 E1t = E2t Tangential component of electric field is continuous
Boundary between two neutral dielectrics D1 If Dn = Dz were discontinuous, then which would contradict
Boundary between dielectric and conductor Et = 0 in the conductor Curl E = 0 still holds Et is continuous Therefore Et = 0 on both sides
A conductor can have surface charge, which is extraneous to the dielectric. E and P are both 0 in the conductor, so D = 0 there. dielectric conductor Surface charge density on conductor = extraneous charge on dielectric
Name and unit conventions Landau, Gaussian Units D = E + 4 P = electric induction D,E,P all have the same units Div D = 4 ex (extraneous charge density) Div E = 4 < >r (total charge density, intrinsic + extraneous) Other books, S.I. units D = 0E + P = electric displacement D,P have the same units, E has different units (V/m) Div D = f (free charge density) Div E = / 0 (total charge density, bound+ free)
