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Homework Help: Dipole layer help

  1. Sep 21, 2003 #1
    (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
     
  2. jcsd
  3. Sep 22, 2003 #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?
    Cheers
     
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