Capacitance and forces for two square electrodes

A numerical and semi-analytical study of electrostatics of a system of two parallel square electrodes is focused on the behavior at short and large distances of the capacity coefficients and of the electrostatic forces between the plates. It is found, using a Boundary Element Method approach with a regular grid and an analytical treatment of the kernel matrix, a strict parallelism with the analogous system of two circular disks, in particular for the possibility of disentangle the divergences at short distances and the presence of a logarithmically divergent repulsive force, with the exception of electrodes with exactly opposite charges. With our semi-analytical approach, fully exploiting the symmetries of the problem and using very small subdomains, the capacitance coefficients of the two square capacitor are determined with a great accuracy, comparable with the best data available in the literature just for the capacitance of a single square