The electric field in dielectrics Section 6

Dielectrics: Constant currents are impossible Constant internal electric fields are possible. No macroscopic currents Macroscopic field Might be locally non-zero

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 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 = 

Total dipole moment of the dielectric i th component surface Sum over j Dipole moment = = dipole moment per unit volume

Still talking about neutral dielectrics Holds both inside and outside (where D = E) “Electric induction” Average r is over charges belonging to the dielectric

If extraneous charges are added, we get a “charged” dielectric Extraneous charge density

Boundary between two dielectrics E 1t = E 2t Tangential component of electric field is continuous = E1E1 E2E2

Boundary between two dielectrics D1D1 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

Even a neutral conductor can have surface charge (but no P) 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)