Re: Q about E-tesla-6

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

Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

> Geofrey,
>         thanks for taking the time
>
> >Because a charge placed on a toroid will not uniformly distribute itself
> >over the surface, I have no idea of how to compute the charge density.
> >Without an expression for the charge density, the calculation of the
> >potential cannot proceed. Anyway I thought it was an interesting question
> >and I'll think about it some more.
>
> OK, glad that at least one person besides myself thinks the charge might
> not distribute itself uniformly over the toroid.
>
> One possible analogy is that the electrons are a "gas" that are in an
enclosed
> volume (the sheet metal aluminum of the toroid is the "volume", not the
whole
> solid toriodal volume), in which case the "pressure" would of course force
> a uniform distribution. But the electrons are not a "gas" they exert a
pressure
> not only to their neighbors but also the inverse-square force across free
space
> to all other electrons in other relatively remote regions of the toroid.

This problem is typically solved iteratively, and then, praying for a nice
closed form solution that happens to solve the infinite series. There isn't
one for spheres.