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From: ix826@sdcc6.UUCP (tim drabik)
Newsgroups: net.physics
Subject: Problem: Find an Electrostatic Green's Function for This Geometry:
Message-ID: <2065@sdcc6.UUCP>
Date: Fri, 10-May-85 11:54:37 EDT
Article-I.D.: sdcc6.2065
Posted: Fri May 10 11:54:37 1985
Date-Received: Sun, 12-May-85 02:37:31 EDT
Distribution: na
Organization: U.C. San Diego, Academic Computer Center
Lines: 40
Keywords: Dielectric slab, Image charges

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
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