Re: capacitance of a disk

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 8 Feb 2001, Carl E. Mungan wrote:

> So what is the capacitance of an isolated disk? Feel free to make
> whatever simplifications or approximations you want and otherwise
> change the problem to make it more tractable or meaningful. Carl

To at least first order accuracy we can take the result for the
absolute potential of a *uniformly charged* disk

  V = Q/(2 pi epsilon_o R)

to approximate that of a charged *conducting* disk and find,
therefore, that

  C ~= 2 pi epsilon_o R

A conducting disk should actually have a slightly lower absolute
potential so the correct answer will be somewhat larger; I would
think perhaps 10 to 20% larger.

This compares pretty nicely to that of a sphere which would have
about twice the capacitance for the same size since it has about
twice the area to pack charge onto.

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