E. R. Love's integral equation for the circular plate condenser

Publisher: Cambridge University Press

E-ISSN: 1446-8735|46|1|85-93

ISSN: 1446-1811

Source: ANZIAM Journal, Vol.46, Iss.1, 2004-07, pp. : 85-93

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Abstract

In a classical paper, E. R. Love considered a certain function defined by a singular integral which is harmonic outside a circular disk. Love's objective was to derive a simple integral equation whose solution leads to a useful formula for the capacitance of the condenser consisting of two parallel circular plates. We close a gap in Love's derivation by finding a new nonsingular representation of Love's singular integral which permits one to draw the required conclusions about its boundary values and thereby establishes the correctness of Love's expression for the capacitance.