Numerical and analytical results for the two disks capacitor problem

Abstract

In this paper we study the two disks capacitor, for equal and different radii. The new results obtained allow a complete characterization of capacity coefficients and forces at short distances. An extensive numerical calculation confirms the theoretical results. The study shows the existence of a hierarchy in the divergent behavior of the capacitance coefficients and this implies some unusual behavior of the forces, strictly related to the dimensionality of the near-contact zone between electrodes.