Parallel Plate Capacitor -- from Eric Weisstein's World of Physics

Given plates of area A separated by a distance d (and ignoring edge effects), the capacitance in cgs is

In MKS, the capacitance is given by by

where is the permittivity of free space.

Kirchhoff's formula for a circular parallel plate capacitor in cgs including edge effects is

(Landau and Lifschitz 1987, p. 19).

For sinusoidally driven circular plates, the electric field E must obey the wave equation

where c is the speed of light. In cylindrical coordinates, the solution is

where is a Bessel function of the first kind Eric Weisstein's World of Math, is a Bessel function of the second kind, Eric Weisstein's World of Math k is the wavenumber, is the angular frequency, and A and B are constants. Using the boundary condition

so the solution is

Capacitance, Capacitor

References