APPROXIMATE EVALUATION OF CAPACITANCES BY MEANS OF GREENS RECIPROCAL THEOREM

The application of Green's reciprocal theorem to a system of two condu ctors forming a capacitor leads to an analytical expression for the ca pacitance that involves the equilibrium charge density on the surface of one conductor. This unknown density can be approximated on the basi s of physical arguments (in the simplest case, with a constant) or wit h the aid of Thomson's theorem. The method is applied to the evaluatio n of the capacitance of the sphere-plane system and the parallel disk capacitor, and is shown to yield fairly accurate results. For the latt er capacitor, the constant density approximation yields a maximum devi ation of about 7% from recently published numerical values; an improve d density is also proposed that yields agreement within 1.5%. (C) 1996 American Association of Physics Teachers.