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Asymptotic formula for the capacitance of two oppositely charged discs

Published online by Cambridge University Press:  24 October 2008

W. C Chew  and
J. A Kong
W. C Chew
Affiliation:
Massachusetts Institute of Technology
J. A Kong
Affiliation:
Massachusetts Institute of Technology
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 373 - 384
Copyright
Copyright © Cambridge Philosophical Society 1981

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