Re: Spheres vs Toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:

 > Original poster: "Godfrey Loudner" <ggreen-at-gwtc-dot-net>

 > The book "Field Theory For Engineers, Moon and Spencer, Van Nostrand, 1961"
 > calculates a "Legendre" type expression for the potential P surrounding
 > a torus. I imagine you can get the field using E = -grad(P). This expression
 > for P is used to get the exact formula for the capacitance of a torus.
 > The pages are 368 to 376. Do you want me to scan and send? Right now, I
 > don't
 > know what would happen to this expression for E as you descend to the
 > surface
 > of a torus. I have to check that out over the next few nights.

This would be interesting. There is something that looks like this in
the "Circular 544", but the text is somewhat obscure. I found also some
materials in the web, after observing that those functions are better
known as "toroidal functions". I found even some of the original papers.
(Search for "toroidal functions" in gallica.bnf.fr and you will find a
paper from 1881 that apparently has solutions for potential,
capacitance,
etc, in a different notation).

Antonio Carlos M. de Queiroz