TY - JOUR

T1 - Asymptotic formula for the capacitance of two oppositely charged discs

AU - Chew, W. C.

AU - Kong, J. A.

N1 - Funding Information:
This work was supported by Schlumberger Doll Research Centre Services Electronics Program under Contract DAAG29-78-C-0020.

PY - 1981/3

Y1 - 1981/3

N2 - 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.

AB - 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.

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U2 - 10.1017/S0305004100058242

DO - 10.1017/S0305004100058242

M3 - Article

AN - SCOPUS:84971138029

SN - 0305-0041

VL - 89

SP - 373

EP - 384

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -