Re: Confused by a derivation.

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Berkeley Physics Course did it, but they only give the result:
 The true cap. ....
effect of edge correction ... represented by ...

Q = [A (potential 1 - potential 2)/4Pi*s ] * f  where f is ratio of
separation (s) to radius of disks (R)


s/R and f respectively:    0.2 - 1.286;  0.1 - 1.167;  0.05 - 1.094;
0.02 - 1.042; 0.01 - 1.023

bc

BTW  found more recent determination of limits on n=2    Williams,
Faller, and Hill '71

David Bowman wrote:

> Regarding John Mallinckrodt's comment:
> > ...
> > 1 that we genuinely do have planar symmetry, i.e., there is no
> >  fringing field (this is the key), and
> > ...
> > For real capacitors assumption 1 is violated and the result does
> > not hold although the violation is typically quite minor.
>
> Since last year I was able to find the exact expression for the
> capacitance to infinity of a thin circular disc, I thought I
> might try my hand at trying to exactly solve for the capacitance
> of a pair of parallel oppositely charged circular plates so as to
> see explicitly and analytically the effects of the fringing field
> as a function of the plate separation.  So far I haven't come up
> with a solution.  But if I do, I post it.  Maybe the exact solution
> is just too hard; we'll see.  So far it's too soon to tell.
>
> David Bowman
> David_Bowman@georgetowncollege.edu