RE: Q about E-tesla-6

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

Original poster: "Loudner, Godfrey by way of Terry Fritz <twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>

Hi Peter

I am responding to your question regarding an exact formula for the self
capacitance of a toroid. One would have to center a toroid inside a sphere
of radius r, and compute an expression for the potential difference between
the toroid and the sphere. Once such an expression is in hand, one can give
an expression for the capacitance of the arrangement of the toroid and the
sphere. Then the self capacitance of a toroid can be obtained by finding the
limit of the capacitance expression as r approaches positive infinity. 

Using toroidal coordinates, the surface integral to compute the potential
can be set up in terms of the charge density on a toroid. Once an expression
for the charge density is in hand, I am betting that the resulting integrals
will be so horrific that they cannot be evaluated in terms of familiar
special functions.

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.

Godfrey Loudner  

> -----Original Message-----
> From:	Tesla list [SMTP:tesla-at-pupman-dot-com]
> Sent:	Monday, September 10, 2001 8:02 PM
> To:	tesla-at-pupman-dot-com
> Subject:	Q about E-tesla-6
> 
> Original poster: "Peter Lawrence by way of Terry Fritz
> <twftesla-at-qwest-dot-net>" <Peter.Lawrence-at-Sun-dot-com>
> 
> Terry,
>       I've started using E-Tesla-6, and have read your short overview
> about
> it but I have some questions about its design.
> 
> I think I understand how the electric field is computed at any point (the
> sum
> of the electric fields from the charge at many individual points for all
> the
> TC "parts"), but how is the distribution of charge on a toroid computed -
> do
> you assume it is evenly distributed over the entire surface of the toroid
> plus
> the center plate, or is there an iterative method to determine the charge 
> distribution, or is there a known formula?
> 
> I am wondering both to understand E-Tesla-6, and because I would be
> interested
> in knowing how an "exact" formula for the free-space capacitace of a
> toroid
> could be determined, I've seen the derivation in physics books for a
> sphere,
> but never anything more complicated.
> 
> thanks,
> Peter Lawrence.
> 
>