Re: visualizing fields near charged objects

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Fri, 9 Feb 2001, Ludwik Kowalski wrote:

> 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

You don't want to (and really can't, I think) go there with a 2-d
spreadsheet.  Fortunately, the isolated disk capacitor has
azimuthal symmetry so all derivatives in the phi direction vanish.

The spreadsheet universe for this problem is a plane that includes
the symmetry axis and the full 3-d picture emerges by rotating it
around that axis.

Similarly BTW, In the usual 2-d cartesian relaxation scheme, we
implicitly assume no out-of-the-plane variations.  John D's "dog"
is not, therefore, "one block thick." It is a cross sectional
slice of a structure that is extended infinitely in both
directions in and out of the plane.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm