# 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

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:
>
> 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

```