Re: eddy current with secondary coil

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

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

Tesla list wrote:

 > Original poster: Ed Phillips <evp-at-pacbell-dot-net>

 >         Thanks for the reply.  Has anyone ever worked out the complete 
solution
 > including effect of capacitance on current distribution?  Are the
 > effects significant enough to be considered in normal design work?

Very probably, no. The "exact" solution, if someone reached it,
is almost surely too complicated to be more useful than the results of
numerical simulations with finite elements. Papers dealing more
or less well with the subject can be found since 100 years ago or more.
Paul Nicholson was doing something about the problem.

Just consider a possible "simple" model:
A coil can be decomposed in a series of circular loops, an approximation
that works well for inductance calculations. The calculations of
inductances and mutual inductances is then no great problem (my
program works in this way). To add capacitances, the capacitances
of the rings to ground and among them (maybe these can be ignored)
shall be calculated. This is possible (I didn't try yet), but not
trivial (remember the complications in obtaining exactly the capacitance
of a toroid). The result would be a huge lumped model, that can be
used for simulations, but to extract something apparently simple as
the "exact" voltage and current profiles along the coil as closed
simple expressions would be difficult.

Complete models for these things would allow precise calculations of
Medhurst capacitance, or of the similar capacitance seen from the
base of the third coil in a magnifier. The exact effect on the
coupling coefficient of a Tesla transformer of the nonuniform
current distribution in the secondary (and maybe in the primary too)
could be predicted.

These fancy calculations, however, are not necessary to make a system
that works very close to the optimal configuration. They just
confirm that we know what is happening.

Antonio Carlos M. de Queiroz