Re: Charged disk; was electrostatic ...

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Chuck Britton wrote:

> A fairly common misconception is that 'most' of the charge will
> collect on the more sharply curved surface, (needle tip). A closer
> analysis will indeed show that the charge DENSITY is quite large on
> the highly curved surface, but the small area involved does NOT lead
> to a preponderance of charge being on the tip. Corona discharge has
> been ruled out in this discussion of an 'isolated' object. Lightning
> rod tips are NOT isolated and do indeed exhibit coronal discharge.

I am willing to accept this. If this is true then the cylinder
approximation (with three well defined surfaces) makes
sense to me.

Can somebody answer this question? Suppose the electrified
object is like a pear. Or more exactly it is a set of two spherical
segments connected smoothly with a truncated cone. Let the
left segment have R1=20 cm, the right segment R2=5 cm and
the distance between the centers of segments 30 cm. There is
nothing special about this geometry; it is an illustration.

We all known that concentration of charges will be higher on
the right "pole" than on the left "pole". But how many times
larger? Factor of 4? Factor of 16? Neither of the above? Is
there any rule of thumb about this?
Ludwik Kowalski