Asymptotic formula for the capacitance of two oppositely charged discs

Abstract

Asymptotic formulae for the capacitances of two oppositely charged, identical, circular, coaxial discs and two identical, infinite parallel strips separated by dielectric slabs are derived from the dual integral equations approach. The formulation in terms of dual integral equations using transforms gives rise to relatively simple Green's functions in the transformed space and renders the derivation of the asymptotic formulae relatively easy. The solution near the edge of the plates, a two-dimensional problem previously thought not solvable by the Wiener-Hopf technique, is solved indirectly using the method. Solution of the Helmholtz wave equation is first sought, and the solution to Laplace's equation is obtained by letting the wavenumber go to zero. The solution away from the edge is obtained by solving the dual integral equations approximately. The total charge on the plate is obtained by matching the solution near the edge and away from the edge giving the capacitance.

A Complete Variational Method for Capacitance Extractions

“…When microwave integrated circuits became important, it was then useful to find the capacitance of two circular disks separated by a dielectric slab [9][10][11][12][13][14]. This geometry is encountered in the microstrip capacitance which forms an important component of microwave integrated circuits.…”

The potential due to a circular parallel plate condenser

“…Many papers have been written in this area, including [6] and [7] which were also directed towards cancer therapy. Most of the papers have concentrated on the case of small separation K, as have [7] and (to some extent) [2] and [3]. These two papers contain extensive bibliographies.…”