The geometrical nature and some properties of the coefficients of capacitance based on the Laplace’s Equation

The fact that the coefficients of capacitance for a set of capacitors are geometrical factors appears in all textbooks of electricity and magnetism. However, in basic treatments there is no a rigorous demonstration of such a fact and most of the proofs are based on the Green formalism. We present a demonstration based on the Laplace’s equation that can be accesible for students of a basic course in electricity and magnetism. Moreover, the formalism developed permits to obtain some properties of the matrix of capacitance that are of both theoretical and practical interest. Finally, some specific calculations of such coefficients are done to illustrate the usefulness of the formulas and properties obtained in the paper.