Re: electrostatic shielding

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Sun, 4 Feb 2001, Ludwik Kowalski wrote:

> No, I did not see it the way in which describe. The disk is
> 3-dimensional but it is not a cylinder. A cylinder has sharp
> edges and I want to avoid them. That is why in my problem
> edges are rounded (radius=0.5*thickness everywhere).
> A strongly oblate ellipsoid of revolution is likely to be a
> more suitable approximation than a cylinder.

Rounding the corners in this manner will, of course, make a
difference, if only because it limits us to consideration of
"disks" that have a "fractional thickness"

   f = thickness/radius <= 2

Note that these "disks" become spheres when f = 2!

It seems most reasonable in this case to call the rounded portion
the "edge" and it seems even clearer to me that, in this case,
thicker disks will have a larger fraction of their charge on the
edge and for essentially the same reason that it is true for disks
with unrounded edges--thicker disks have more edge.  (In fact, the
thickest possible "disk" of this sort has *nothing* but "edge"!)

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm

P.S.  If you *really* want to start looking at ellipsoids of
revolution (and I'm going to strongly suggest that you don't!) you
will want to look at David Jackson's paper, "Charge density on
thin straight wire, revisited", AJP, Volume 68, Issue 9, pp.
789-799, September 2000.