- #1
Norman
- 897
- 4
(Sorry for the duplicate post but I couldn't delete the old one in classical physics and didn't see this forum until I posted the original)
This is a homework question so please do not just tell me the answer, but please point me in the right direction.
A dipole layer, D(y,z), exists on the plane x=0. Find the boundary conditions (discontinuities, if any) for [phi](x,y,z), E_x(x,y,z),
E_y(x,y,z), and E_z(x,y,z) across the plane x=0. In view of this result do you believe in the boundary condition that the tangential component of E is contiuous across a boundary? Review the derivation of the boundary condition and see if and where the derivation breaks down.
When I read the first part of the problem I was content with how to solve it. The potential is discontinuous by D/[epsilon_0]. Then I would argue using typical boundary value knowledge that E_y and E_z are continuous and that E_x should be discontinuous. But after finishing reading the problem, it seems that my so called "notions" of the situation might be incorrect. Where do I start with finding the Electric Field components? I am very confused and any help would be very appreciated.
Cheers
This is a homework question so please do not just tell me the answer, but please point me in the right direction.
A dipole layer, D(y,z), exists on the plane x=0. Find the boundary conditions (discontinuities, if any) for [phi](x,y,z), E_x(x,y,z),
E_y(x,y,z), and E_z(x,y,z) across the plane x=0. In view of this result do you believe in the boundary condition that the tangential component of E is contiuous across a boundary? Review the derivation of the boundary condition and see if and where the derivation breaks down.
When I read the first part of the problem I was content with how to solve it. The potential is discontinuous by D/[epsilon_0]. Then I would argue using typical boundary value knowledge that E_y and E_z are continuous and that E_x should be discontinuous. But after finishing reading the problem, it seems that my so called "notions" of the situation might be incorrect. Where do I start with finding the Electric Field components? I am very confused and any help would be very appreciated.
Cheers