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*From*: Joel Rauber <Joel_Rauber@SDSTATE.EDU>*Date*: Sun, 11 Feb 2001 15:30:01 -0600

David,

Can you provide it as .pdf file somehow? Or allow those interested, me for

instance, to e-mail you for such a file .pdf or MS-Word or Mathematica

(These are what I can handle easily) for an e-mail with file attached. It

does seem that ascii would be gross!

Joel Rauber

-----Original Message-----

From: phys-l@lists.nau.edu: Forum for Physics Educators

[mailto:PHYS-L@lists.nau.edu]On Behalf Of David Bowman

Sent: Saturday, February 10, 2001 1:32 PM

To: PHYS-L@lists.nau.edu

Subject: Re: capacitance of a disk

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

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