ix826@sdcc6.UUCP (tim drabik) (05/10/85)
Consider a two-dimensional medium (homogeneous in the 3rd dimension) with a one-dimensional permittivity variation: eps1 ________________________________ ^ eps2 h ________________________________ v eps3 The problem is to find an analytical expression for the potential everywhere due to a unit charge placed anywhere. Remember, this is a two-dimensional problem, so phi must satisfy div(eps(r) * grad phi(r)) = -4 * pi * delta (r - rprime) where div, grad, and r are two-dimensional. Simplifying assumptions allowed are: eps1 = eps3 = 1, and the assumption of SCALAR permittivity (if you can solve it for anisotropic eps2, I'll buy you a beer). Hints: The potential of a charge between plane conductors can be found using an infinitude of image charges. The problem arose from a consideration of electrooptic modulator performance. I'll post a correct solution if I get one (I'm still working on it myself). Tim Drabik UCSD Applied Physics ...sdcc6!ix826 ...sdcc12!drabik