CAPACITANCE MATRIX REVISITED

The capacitance matrix relates the potentials and the charges on a system of conductors. We review and rigorously generalize its properties, block-diagonal structure, inequalities and regularity, deduced from the geometry of the system of conductors and analytic properties of the permittivity tensor. Furthermore, we discuss alternative choices of regularization of the capacitance matrix, which allows us to find the charge exchanged between the conductors having been brought to equal potential. Finally, we discuss the approximations utilized in calculations of the capacitance of capacitors connected in parallel and series.