Re: Charged disk; was electrostatic ...

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

Leigh Palmer wrote:

> > No, I do not disagree; you can make a disk which is more or
> > less cylinder-like. My intuition suggests that a cylinder with
> > very sharp edges will have most of its Q near the edges.
>
> I don't see why you say that. Do you believe that there should be
> any important difference arising in the charge distribution on a
> 1 cm long, 1 cm diameter cylinder if its edges go from 1 nm radius
> of curvature to 10 nm? My intuition tells me that there will be no
> important difference.

OK, that is where we are making different predictions. I expect that
the difference will be significant. Here is an analogy. Start with a
metallic sphere which has some charge Q. It is uniformly distributed
over the smooth surface. Now supply the same Q to another sphere
of the same radius which but has a sharp needle sticking out. Will
most of the Q be concentrated near the sharp point? I would say yes.
Each sharp edge of a cylinder is like a set of many needles. But
I am not at all certain that this is correct because curving along the
edge is much less rapid than curving across the ridge.

> > The S(r) distribution will be like a delta function. But why
> > should my intuition be trusted? I am only saying that a real
> > disk is not a mathematical cylinder.
>
> I believe the mathematical solution results in a convergent
> fraction of the charge on, say, the outer ten percent of the
> area of the disc. John's simulation suggests a finite charge
> density resides in the center.

A 2D analog of a needle is a triangular shape. I would expect
equal concentrations of charges near sharp points when the
triangle is equilateral. For a triangle with one very small
angle, say 1 deg, I would expect a big fraction of Q near
this one sharp point.

Doesn't this discussion remind you of a medieval debate on
how many angels can reside ...? We need a 3-D simulation.
Ludwik Kowalski