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# Re: visualizing fields near charged objects

A partial answer to this question is that one must develope a finite
difference scheme to approximate the laplacian in these coordinates. Some
references that are readily available and may be of partial help.

Abromowitz & Stegun: section 25 around page 877

This is a Dover publication titles "Handbook of Mathematical Functions"

CRC 30th ed. math tables around page 705-715, the section on numerical
differentiation.

Hope this may be of some help.

Joel Rauber

-----Original Message-----
From: phys-l@lists.nau.edu: Forum for Physics Educators
[mailto:PHYS-L@lists.nau.edu]On Behalf Of Ludwik Kowalski
Sent: Friday, February 09, 2001 8:28 AM
To: PHYS-L@lists.nau.edu
Subject: Re: visualizing fields near charged objects

And what is the corresponding formula for "a" when it has
six neighbors (3-dim)? Suppose f and g are added in the phi
direction. I do not trust myself in trying to answer this
question on the basis of the general theoretical formula.
Ludwik Kowalski

John Mallinckrodt wrote:

On Fri, 9 Feb 2001, John Mallinckrodt wrote:

where r_a is the radial index for cell a. Setting the Laplacian =
0 and solving for a we get

a = (b+c+d+e)/4 + (c-e)/(2*r_a)

Oops! I should have said:

a = [ (b+c+d+e) + (c-e)/(2*r_a) ]/4