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

The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplace's equation that is accessible for an intermediate course on electricity and magnetism. The properties of Laplace's equation permits to prove many properties of the capacitance matrix. Some examples are given to illustrate the usefulness of such properties.