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*From*: brian whatcott <inet@INTELLISYS.NET>*Date*: Sat, 10 Feb 2001 15:29:42 -0600

At 14:32 2/10/01 -0500, you wrote:

According to my analytic calculations the capacitance (to infinity)

of a circular disk of radius R and thickness 0 is a solvable problem, and

the *exact* answer is:

C = 8*[epsilon]_0*R

or equivalently, the capacitance of a disk of 1 meter diameter is about

35.41675127... pF.

This makes the capacitance of the disk 27.32395...% greater than half

that of a sphere of the same radius.

BTW, in case anyone is interested, I solved the problem by making a

transformation to a coordinate system whose surfaces of constant

coordinate were a nested family of confocal oblate spheroids that were

locally orthogonal to another confocal nested set of hyperboloids of

revolution (of one sheet). The third coordinate was the usual azimuthal

angle about the symmetry axis of these surfaces. The problem was

solvable because the innermost spheroid was degenerate with an

eccentricity of 1-- yet having a finite semimajor axis. This innermost

degenerate surface was the disk of interest (which had to be an

equipotential surface). The overall potential in space depended only

on the coordinate that labelled the confocal spheroids, and each one was

a surface of constant potential. The also automatically means, BTW, that

the problem of the capacitance of any oblate spheroid of arbitrary

eccentricity is also exactly solvable. If anyone is interested I can

post the potential function (after it is reconverted back to spherical

coordinates), but it is quite a mess to try to reduce to ASCII notation,

so I hesitate to post it unless there is sufficient curiosity about it.

David Bowman

David_Bowman@georgetowncollege.edu

Magnificent! Will you publish this result as a short note in a scientific

periodical please? Were you able to glimpse insights into analytical

methods for the polygon by any chance?

brian whatcott <inet@intellisys.net> Altus OK

Eureka!

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