Re: electrostatic shielding

[Leigh Palmer <palmer@SFU.CA>]

At 10:28 AM -0800 2/4/01, John Mallinckrodt wrote:
> I think that by "finite size" you really mean to say "nonzero
> thickness" and that you mean to compare the fraction of the charge
> that is on the "ends" (the two circular portions of the disk
> surface) to that on the "edge" (the cylindrical portion.)  If so,
> I remain very confident that that fraction on the "edge" will be a
> monotonically increasing function of the "thickness to diameter"
> ratio for the reasons that I stated in my previous message.  At
> the very least, I think it is manifestly evident that virtually
> all of the charge resides on the "edge" of a long thin wire which
> is nothing more than a VERY thick disk.

That works for me, too. Take John's wire to a cylinder with, say, a
1:1 length to diameter aspect ratio, with a (constant) charge Q.
Shrink the cylinder in length and the surface charge density at the
centers of the circular ends of the cylinder will steadily increase
as charge is repelled from the increasingly dense charge near the
edge. The rate of increase in charge density at the center  will go
to zero, and the charge density, itself, to a finite limit, as the
thickness of the disc goes to zero.

I think that this sort of argument is very illuminating when
approaching any physical problem. Some very wise physicist (whose
name escapes me) once said something like "Never start a calculation
before you know the answer." He (I'm sure it was a "he") was a fine
theoretician. I'm sure that someone in this group can supply the
correct quotation and attribution.

Leigh