Abstract
A simple approximate solution is derived for the current and potential distributions around a sphere gap with small separation. The method is based on the fact that the problem has an elementary solution for two equal spheres in contact. Its accuracy is about 1% for ratios of gap/sphere radius not greater than 0·1. Explicit elementary expressions are obtained for the stress distribution, the total conductance for spheres and segments of spheres, the fraction of the total current flowing within a given radius from the axis, and the same fraction within a radius having a specified ratio of stress to maximum stress. The implications of the results are discussed in relation to measurements of the dielectric properties of liquids and solids.
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