RE: Spheres vs Toroids

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

Original poster: "Godfrey Loudner" <ggreen-at-gwtc-dot-net> 

Yes indeed. Upon checking out the latest I could find on values, we have

u = 4Pix10^(-7) NA(-2) exact and c = 299792458 m/s exact. Then use

epsilon = 1/uc^2.

My estimate say to use 69 terms to get 20-place value accuracy. To be sure,
I
used 100 terms. In my Mathematica session, I asked for 20 significant
figures;
which in the case of D = 90 cm and d = 30 cm, translates to 18-place value
accuracy. Using Mathematica, I get 40.583973310804090804 pf.

Attention to the accuracy of epsilon is important. I guess Antonio will be
fixing
his program.

Godfrey Loudner


You wrote:

  > I have just finished a routine that calculates exact capacitances
  > of toroids in free space.

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

A better value is 40.583978.  Yours is slightly in error
because you haven't used enough decimal places for epsilon.

Multiply your answer by 8.854188/8.85 to get the correct value.
--
Paul Nicholson
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