Solid State Tesla Coil Book Available

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

Hi All

In page 8 of chapter 2, Dr. Johnson speculates that equation 21 is too high
by a factor of pi. Equation 21 gives an elegant formula for the capacitance
of an isolated toroid. The capacitance formula is taken from the book "Field
Theory For Engineers, Moon and Spencer". A sketched of the derivation of the
capacitance formula is given by Moon and Spencer, but not enough details are
given to follow the calculations involved. To see if Dr. Johnson's
speculation was correct, I carried out the calculations in detail. The
result is that Dr. Johnson is correct. The factor pi must be removed from
equation 21 on page 8 of Dr. Johnson's book. Because Moon and Spencer repeat
the error in three equations, the error is more than just a typo. The error
results from failing to cancel pi in one of the steps. 

The following corrections must be made in Moon and Spencer.

Page 373 (second equation from the top), replace V / 2 by V / pi. This error
is a typo and does not cause another error in the next step. 

The factor pi must be removed from page 375 (second equation from the top),
page 375 (equation 13.29), and page 376 (equation 13.29a).

The details of the calculation are rather involved, but are greatly
simplified if one uses a sort of commutator relation between the derivatives
of Legendre functions. The commutator relation makes it possible to get by
without actually writing out expressions for the derivatives of Legendre
functions. It took me awhile to realize that I could apply the commutator
relation. 

Software packages such as Mathematica can calculate values of the
capacitance formula to any degree of accuracy. Unfortunately the Mathematica
package cost about $1,600 (half that to an educational institution).

Anyway I'm playing around with approximation theory to see if I can extract
a useful algebraic formula that approximates the capacitance formula given
in Moon and Spencer. If I'm lucky, I'll share the result with the list. 

Godfrey Loudner