ANZIAM J.
46 (2004), 85-93
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E. R. Love's integral equation for the circular plate condenser
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Edgar Reich
School of Mathematics
University of Minnesota
Minneapolis, Minnesota 55455
USA
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.
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