Maxwell's equations on the boundary between non-conductor and conductor

[Mingfeng]

Homework Statement

Hi, this is the first time I post a thread in this forum.
I am not sure if I could post this question here since it is not a homework problem.

I have trouble understanding two boundary condition between nonconductor and conductor from Maxwell's equations in dynamic case.

First, n X (H1 - H2) = I (media 1 is non-conductor, media 2 is conductor)
I know that when the conductor is perfect, there is discontinuity on the boundary since H2=0. So there is surface current K.

when the conductor is regular conductor, I = J . da = 0 because we take the limit as da -> 0 when we get the equation n X (H1 - H2) = I. Is this reasoning right?

And when the conductor is superconductor, is H continuous between the boundary?
Is there surface current K?



Second, (D1 - D2) . n = σ ,

When the conductor is perfect, there is discontinuity on the boundary since D2=0.

What happen when the conductor is regular conductor?
Does D1 = D2 ? Is there and surface charge?

And What happen if it is superconductor?
Does D1 = D2 or D2=0, D1=σ ?


Thanks.

Homework Equations

The Attempt at a Solution

 

[Nate810]

1. For the n X (H1 - H2) = I equation, when the conductor is a regular conductor, there is no surface current K, because as you said, we take the limit as da -> 0 when we get the equation, so I=J.da=0. However, there might still be some surface current, depending on what type of material is at the boundary. When the conductor is a superconductor, there is no surface current at the boundary since all the electric field is zero inside the superconductor. The H field is continuous across the boundary, though, since there is no discontinuity in the magnetic field.2. For the (D1 - D2).n = σ equation, when the conductor is a regular conductor, the D field is not necessarily equal to each other at the boundary. The surface charge will depend on the type of material at the boundary and the electric field present in each medium. For a superconductor, the D field will be equal to each other at the boundary, but the electric field will be zero, so there will be no surface charge.