# Re: Sphere/Toroid Comparison Chart

```Original poster: "Malcolm Watts by way of Terry Fritz <twftesla-at-uswest-dot-net>" <m.j.watts-at-massey.ac.nz>

Hi Luc,

On 9 May 01, at 20:51, Tesla list wrote:

> 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

I would have thought it was about e.s. field rather than charge
distribution?? Suppose you have a toroid charged to some voltage. You
can't argue that charges are unevenly distributed over its surface as
there would be a potential difference between portions of a conductor
and hence a current flow without any input of energy. Y-N? The
portions of the toroid facing each other will have a minimal nett
electric field between them. Or is my inderstanding incomplete?

Malcolm

> P.S. I need to try to understand the electrostatic equations ;-)
>
> Tesla list wrote:
> >
> > Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>"
> <Mddeming-at-aol-dot-com>
> >
> > In a message dated 5/8/01 8:17:07 PM Eastern Daylight Time,
> > tesla-at-pupman-dot-com writes:
> >
> > >
> > > Original poster: "Luc by way of Terry Fritz <twftesla-at-uswest-dot-net>"
> > > < ludev-at-videotron.ca>
> > >
> > > Hi guy
> > >
> > > I post again the same question: If you look at the chart you'll
> > > see that until you hit 18" of exterior diameter the toroid with a
> > > thickness of 4" have more capacity than one of 6" thickness.
> > > Please could some of you explain to me how a toroid with an area
> > > bigger could have a smaller capacity. I already know that the
> > > surface facing the center ( the hole of the donut ) don't
> > > participated as far as the exterior. But the exterior of a 6"
> > > thick toroid is bigger than the area of a 4" one.
> > >
> > > Tx
> >
> > Hi Luc, All!
> >
> >         I was wrong about the C-C diameter. It is actually the
> >         exterior
> > diameter. I believe the mystery of the smaller toroid can be
> > explained like this: For a given major diameter, the toroid with the
> > larger chord will have a smaller inner diameter, meaning the
> > curvature around the donut hole is tighter. For the smaller inner
> > diameter of the toroid with the larger chord, there is greater
> > repulsive force between the charges on the inside curve which
> > reduces the effective capacitance until that inner diameter becomes
> > large enough that the effect is negligible. The smaller the inner
> > diam., the more distorted the charge distribution. A 14" outer
> > diameter toroid with a 4" chord (6" id) actually has more of its
> > surface at a greater distance from the center than one with a 6"
> > chord and 14" outer diameter (2" id). The formula, as an
> > approximation, also allows for negative inner diameters to be
> > computed, which is of course, silly. Matt D.
>
> >
> > Original poster: "Kurt Schraner by way of Terry Fritz
> <twftesla-at-uswest-dot-net>" <k.schraner-at-datacomm.ch>
> >
> > Hi Luc, Bart,
> >
> > ...you are right Luc, of course! - I did an E-Tesla6 calculation for
> > a small coil (2"/10" secondary), supposing a 12"/4" vs. a 12"/6"
> > toroid, and got:
> >
> >           Problem:  Medhurst    E-Tesla6    Diff=~
> > d1   d2   C.bert.P.  C.sec.     C.total     C.toro  Fres
> > (inches)   pF         pF         pF          pF      kHz
> > 12"  4"   13.262     4.153      15.116      10.963  522.27
> > 12"  6"   11.585     4.153      16.350      12.197  502.17
> >
> > Up to now, I was very close to the measurements on my coils, with
> > Bert Pools equation. But those were not in the same range of toroid
> > data. So, reading your first poster, was not recognized well enough
> > (by me). I guess, we are just outside of the validity limits for the
> > (probably-; if Bert is reading, he might comment!) semi-empirical
> > Bert Pool's equation. This equation may well be continued to use in
> > "normal" TC-design procedures, but when it comes to somehow extreme
> > toroids or toroid vs. secondary situations, not be the method of
> > choice. The real things are something like the super-cool
> > measurements of Bart Anderson, which obviously support the use of
> > E-Tesla6. More of this kind of measurements, together with the
> > outcome of the TSSP, will probably lead to design procedures, which
> > are more precise, but, perhaps, more important: applicable to a
> > broader range of TC-parameters.
> >
> > Cheers
> >        Kurt Schraner
>
>
>
>

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