Mutual inductance and K factor

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Original poster: "Loudner, Godfrey by way of Terry Fritz <twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>

Hi All

Using Neumann's formula, I once wrote down an expression for the mutual
inductance between a flat spiral and a single layer solenoid. Curiously I
was never sure that I used Neumann's formula correctly. Assuming I had a
good expression for mutual inductance, I attempted to calculate the
integrals. I believed that an integration was possible in terms of theta
functions. Then the theta functions could be calculated using packages like
Mathematica or Maple. I tried many mathematical tricks, but could not pull
off the integration. These postings have revived my interest in the project,
but in a different direction. I e-mailed Dr. Rzeszotarski asking for his
integral expression for mutual inductance. I want to compare his expression
with my expression just to see if I was on the right track. Also I want to
attempt a derivation of a very useful approximation formula for mutual
inductance. An exact formula seems to be out of the question, but I still
believe one exist in terms of theta function. I don't know if Dr.
Rzeszotarski will send me his integral expressions. If not, I'll proceed
with my own integral expression. Dr. Rzeszotarski performs a numerical
integration of Neumann's formula and that is good enough if one wants a
value. But its a mathematical challenge to try and find an approximation
formula that is good over a wide range of input values. Even if I am not
successful, its always fun to play around with these things.  

Godfrey Loudner