Departures from Coulomb's law displayed by two electrostatically interacting conducting balls are examined in detail. By computing forces on the balls as a function of the ball separation, it is found that at short separations a switch from repulsion to attraction occurs in the general case of arbitrary, likely charged balls. The only exception is the case in which the charges of the balls are related as the squares of their radii: such balls always repel each other. For identical balls of equal charges in magnitude, asymptotic short-separation relations for energies and forces are found. For most of the results obtained the self-similarity property is shown to apply.
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