Re: funny capacitor (SPACE CHARGE)

[Bob Sciamanda <trebor@VELOCITY.NET>]

On Sat, 17 Mar 2001 21:03:16 -0500, Ludwik Kowalski
<KowalskiL@MAIL.MONTCLAIR.EDU> wrote:

> Hi Bob: . . .
> In an earlier electrostatic thread, JohnD was mentionning
> space chages. Can my little universe be set up to illustrate
> a situation in which a space charge is part of the solution?
> If so then please describe the setup for my 400 cells.
> Ludwik Kowalski


I offer this two dimensional finite element version of Poisson's equation
in rectangular x,y coordinates:

V(i,j) = {V(i-1,j)+ V(i+1,j) + V(i,j-1) + V(i,j+1)}/4 + Q(i,j)/(4*eps*dx)

Q(i,j) is the signed amount of charge in cell (i,j)
dx is the cell spacing - assumed equal in both x and y directions.
eps = epsilon.

Note that where Q(i,j) = 0 this is the Laplace (averaging) algorithm.
Corrections/comments are invited.

Bob Sciamanda (W3NLV)
trebor@velocity.net