|Sep21-03, 08:20 PM||#1|
Dipole layer help
(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.
|Sep22-03, 06:59 PM||#2|
Well, I guess no one knew how to solve this (so it goes with internet help I guess).
Anyways here was my solution method:
You know that the potential has a discontinuity of D/[epsilon_0]. Since you are looking at an infinite plate of charge (think of dipole layer as a sheet of positive sigma, parallel and infinitely close to a sheet of of negative sigma.) By symmetry, if you were to rotate the sheet still in the x=0 plane, the Electric Field should not vary, since we are talking about a dipole layer that doesn't vary with position. Therefore the Electric Field should only be in the x direction. Therefore, E_y and E_z are both zero. The x component of the Electric Field (E_x) has a discontinuity of 2*[sigma]/[epsilon_0] at x=0 boundary. This is seen by carefully examining the field inside and outside our boundary.
Sorry this is abreviated, have to teach in a couple of minute.
Anyone know if this is correct?
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