Numerical and analytical results for the two disks capacitor problem

TL;DR

This paper provides a comprehensive analysis of the two disks capacitor, deriving new theoretical results for capacity coefficients and forces at short distances, supported by extensive numerical validation.

Contribution

It introduces new analytical characterizations of capacity coefficients and forces for two disks capacitors with equal and different radii, revealing a hierarchy in divergence behavior.

Findings

Hierarchy in divergent behavior of capacitance coefficients

Unusual force behaviors related to electrode contact zone dimensionality

Numerical calculations confirm theoretical predictions

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.