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

Published online by Cambridge University Press:  17 February 2009

Edgar Reich
Edgar Reich
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA; e-mail: reich@math.umn.edu.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 1 , July 2004 , pp. 85 - 93
Copyright
Copyright © Australian Mathematical Society 2004

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