Re: Inductance of a conical coil

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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: "Godfrey Loudner by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <ggreen-at-gwtc-dot-net>
 >
 > Hello Antonio
 >
 > I haven't yet worked directly with integrating Neumann's integral.
 > In my initial approach, the secondary and primary are modeled by
 > a collection of filament circles. In a vague description, I integrate
 > across a "sheet" of elliptic integrals to obtain an approximate M.

My program is integrating a double integral, similar to one that
appears in Maxwell's book, used there to compute the mutual
inductance between two wire loops. The book shows a solution in
term of elliptic integrals (item 701, page 338). I use a parametric
description of the coils a spirals and end with a similar integral,
with some additional terms to account for the vertical and horizontal
twisting of the loops.
That integral is called Neumann's formula in some texts, but there
are several other formulas with this name, including a double
volumetric integral that calculates self-inductances, that looks
the same but isn't.

 > I'm trying to optimize this circle approach. In the next level of
 > approximation, I'll try and remodel the primary as a collection
 > of circular rings to account for thick primary conductors. The
 > optimized M from the circle approach will play a role in the
 > ring approach. At least with circles and rings, I can move the
 > mathematics along. My goal is a good approximation formula
 > that you can carry in your pocket. I think tonight I'll set up
 > the Neumann's integral for Bart's old 12.75" coil, using a
 > parametric representation of the spiral. Of course I'll use
 > filaments for the conductors. I want to see if the powerful
 > Mathematica software will numerically integrate the Neumann
 > integral.

For mutual inductances, if the coils are at a reasonable distance,
the integration doesn't present problems.

Antonio Carlos M. de Queiroz