Re: topload questions

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:

 > Original poster: "by way of Terry Fritz <teslalist-at-qwest-dot-net>" 
<Mddeming-at-aol-dot-com>

 > >Actually, a single thin wire loop has great part of the capacitance of a
 > >solid toroid (or even a solid ball) with the same diameter.
 >
 > Hi Antonio & all,
 >         I was intrigued by this statement and tried calculating the
 > capacitance of a topload of 16" OD with chord diameters of 0.1" (wire) to
 > 8.0" (0" ID). The results are shown below: Note 16" is the outer diameter
 > of the toroid, not the C-C diameter.
 >
 > Chord ID Cap. % of Max
 > Diam           (pF)      Cap.
 > 0.1 15.80 3.98 22.4%
 >...
 > 1.0 14.00 11.68 65.6%
 >...
 > 7.0 2.00 16.56 93.0%

 > I guess the interpretation of the result depends upon the exact definition
 > of "great part of the capacitance".

You apparently used an empirical formula to compute the capacitances.
I tried Fantc, that uses a precise numerical method, and got, for
the elements floating in space:

16"          sphere: 22.54 pF  (should be 22.60 pF)
16" x 7"     toroid: 19.14 pF
16" x 1"     toroid: 13.94 pF
16" x 0.1"   toroid: 10.18 pF
16" x 0.01"  toroid: 9.4 pF
16" x 0.001" toroid: 9.3 pF
16"          disk:   14.24 pF

I am not sure about the precision of the calculations for the thin
toroids,
but they agree with what I can measure.
The "great part" is close to 50%, tending to 41% of the sphere
capacitance
for thin wire.

Fantc takes forever to analyze the 16" x 0.001" case, and in all cases
lists a strange number as "exact value" (why?).

Antonio Carlos M. de Queiroz