I believe the problem of the polarizability of a generic spheroid
(ellipsoid of revolution) is solvable. A disk is a limiting case of an
oblate spheroid where the eccentricity approachs unity. The opposite
limit of the eccentricity approaching zero is the case of a sphere.
But, I believe, the whole family of spheroids is solvable. We actually
discussed a similar problem on this forum a number of years back. In
that discussion the problem of the capacitance to infinity of a spheroid
was discussed (and also, I think, the case of a confocal spheroidal
capacitor, i.e. a capacitor whose two conductors are the surfaces of a
pair of confocal spheroids).
David Bowman
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Bernard
Cleyet
Sent: Friday, February 23, 2007 4:01 PM
To: PHYS-L Maillist
Subject: [Phys-l] Disc polarizability
In Strong's text Hull claims the polarizability of a metal disc is (2/3)
the permitivity (space) times its diameter cubed. Finding this for a
sphere and even an infinite cylinder is trivial (once one has seen it
done). But a disc, no. Anyone know how it's done (not numerically)?
I've looked in many texts *, googled and not found it.