Re: Spheres vs Toroids

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Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Hi:

I have just finished a routine that calculates exact capacitances
of toroids in free space. The routine uses that series with
Legendre functions, that is not after all so difficult to evaluate
with precision. The values that I am obtaining, however, are a bit
different from the ones that I see in the document prepared by
Gary L. Johnson (that I don't remember from where I obtained).
The formula is the same, but I am evaluating the functions in a
different way, using elliptic integrals, that should be almost
exact.

Example:
Major diameter: 90 cm
Minor diameter: 30 cm
I get: Exact capacitance: 40.5648 pF (all the digits correct)
The document lists:       40.46   pF

(Of course, the difference is insignificant for practical
purposes, but I want the calculations correct.)

There is also a table in the documentation of the program Mandk,
but that table appears to use an approximate formula, the same
listed in Gary's paper.

Antonio Carlos M. de Queiroz