Exact closed-form solution for the electrostatic interaction of two equal-sized charged conducting spheres

Abstract

We provide an exact closed-form solution for the electrostatic interaction of two equal-sized conducting spheres. We calculate the capacitance coefficients for the spheres in terms of the q-analogue of the digamma function. In the near limit, when the two spheres are about to touch, the closed-form exact solutions allow for much faster numerical calculations than the well-known infinite series solutions. By analyzing the exact solution in the near limit, we provide Taylor series expressions for the capacitance coefficients in terms of the surface-to- surface separation of the two spheres.