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>
 >
 > How does the charge distribution on the toroid surface affect the
 > capacitance value?  Certainly the distribution is not uniform as with a
 > sphere?

As most of the charge will be located at the outer side of the toroid,
a thick toroid has more capacitance than a thin toroid with the same
major diameter. A very thin toroid has zero capacitance, but it must
be -very- thin.
That 90 cm toroid has maximum capacitance with minor radius=45 cm,
that just closes the central hole: Cmax = 43.59 pF
With minor diameter=1 cm: 23.69 pF
With minor diameter=0.1 mm: 14.06 pF
A sphere with 90 cm of diameter is the object with this maximum
diameter that has the largest capacitance: C = 50.069 pF
For comparison, a thin disk with 90 cm of diameter has: 31.88 pF
Other comparisons:
Hollow hemisphere with 90 cm of diameter:   40.97 pF
Closed hemisphere with 90 cm of diameter:   42.32 pF

Antonio Carlos M. de Queiroz