Re: visualizing fields near charged objects

[Joel Rauber <Joel_Rauber@SDSTATE.EDU>]

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