Re: Sphere/Toroid Comparison Chart

```Original poster: "Luc by way of Terry Fritz <twftesla-at-uswest-dot-net>" <ludev-at-videotron.ca>

Hi Jim

Tx a lot for the precision, I believe you without any hesitation,
if I understand right; repulsion between 2 electrons vary at the
square of the distance but if you double the number of electrons
on a surface you double the repulsion not quadruple it.

The last time I really play with math is 30 years ago :-( . If
I'm only be able to calculate the effect of an imperfection on a
terminal or the effect of a geometry different than a sphere.

I think I need a big revision of math !!!

Cheers,

Luc Benard

Tesla list wrote:
>
> Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-uswest-dot-net>"
>
> The charge distribution should be independent of voltage (excepting effects
> like space charge or corona).  They are all linear equations so
> superposition should hold.
>
> Where it all breaks down (pun intended, or not), is when the field gets high
> enough to ionize (break down) the air, and that is, most definitely, a
> nonlinear process.
>
> The electrostatic equations are actually quite simple. It's the analytic
> solutions for an arbitrary geometry that are complex (cf. analytic
> expression for E-field between two spheres).  The whole beauty of Finite
> Element Methods (FEM) is that if you break your problem up into sufficiently
> small parts, you can essentially do numerical integration and get an
> approximate answer that is so close to the real thing that it's not worth
>
> The nifty thing these days, with piles of CPU, is that you can run the
> numerical integration multiple times, get a whole raft of data points, and
> then come up with a relatively simple empirically derived equation.  Back in
> the 20's, Medhurst, et al, had to build a pile of capacitors, measure them
> with excruciating precision, etc. Now, you can build those caps (or
> inductors) on a computer, FEM them once, and be done with it.
>
> ----- Original Message -----
> From: "Tesla list" <tesla-at-pupman-dot-com>
> To: <tesla-at-pupman-dot-com>
> Sent: Wednesday, May 09, 2001 7:51 PM
> Subject: Re: Sphere/Toroid Comparison Chart
>
> > Original poster: "Luc by way of Terry Fritz <twftesla-at-uswest-dot-net>"
> <ludev-at-videotron.ca>
> >
> > Hi Matt, Kurt, all
> >
> > Tx guy, both of your answer are logical, I know that
> > electrostatic equations are not particularly easy .... To have a
> > final word on that we probably need measurement and if Matt
> > theory is good; measurement at high voltage ( not sure about that
> > but I think the repulsive force could be higher at higher voltage
> > pushing the charge farther on the exterior ???).
> >
> > Cheers,
> >
> > Luc Benard
> >
> > P.S. I need to try to understand the electrostatic equations ;-)
> >
> > Tesla list wrote:

```