Re: Spheres vs Toroids

["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: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net>

 >> A very thin toroid has zero capacitance, but it must
 >> be -very- thin.
 >
 > I interprete thin to mean small minor diameter and not thin conducting
 > surface.

Yes. Only the shape of the surface is important.

 > Also,  I'm presuming that as the minor diameter go to zero and the
 > toroid/capacitance vanishes, that there is no interconnecting surface that
 > would normally make connection from the center to the inner surface of the
 > toroid contributing to your capacitance calculation.  Would this be correct?

Yes. Otherwise the toroid would be reduced to a thin disk,
that has C=4*e0*diameter in meters. A toroid with the hole closed by
a disk seems a quite complicated object for a closed-form solution.
As a curiosity, The (open) toroid that has the same capacitance of
a thin disk with the same diameter has:

minor diameter = 0.07556682*major diameter.

 > Is the distribution of charge on the outer surface of the toroid (for
 > typical and fixed geometry that we use for TCs) uniform or is there a
 > guassian like distribution across this outer surface.  Does this
 > distribution (whatever it is) affect the capacitance calculation?

The distribution is not uniform. It has a maximum at the outer diameter
and a minimum at the inner diameter, that is zero only if the hole
is closed (Maj. D.= 2* Min. D.). The shape of the distribution, as
far as my studies are, is a complicated series of Legendre functions.

Antonio Carlos M. de Queiroz