Chronology Current Month Current Thread Current Date [Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

# Re: capacitance of a disk

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

C = 8*[epsilon]_0*R

or equivalently, the capacitance of a disk of 1 meter
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