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capacitance of a disk

The discussion of capacitance and of the charge distribution on a
disk seems to have ripened to the point that a question I brought up
in class the other day can perhaps be answered. (I certainly don't
know the answer.)

You can start with two concentric spheres, work out the capacitance,
then let the radius of the outer sphere go to infinity to get the
capacitance of an isolated sphere.

If you try the same thing for a parallel-plate capacitor C = A*e0/d
and let d go to infinity, you get zero which is obviously wrong. I
assume this is because we neglected the fringing field, which is only
valid if d << sqrt(A).

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
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026