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

Mingfeng

1. The problem statement, all variables and given/known data
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.

2. Relevant equations



3. The attempt at a solution