On the change in electrostatic potential energy due to the introduction of an additional conductor

This paper generalizes a result in the classical textbook by Stratton regarding the change in electrostatic potential energy due to the introduction of a conductor S₀ into a fixed system of n conductors of arbitrary shape. The change in electrostatic potential energy is rewritten as a surface integral over S₀ which connects the unperturbed problem (the electrostatic setting before S₀ is introduced) and the perturbed problem (the electrostatic setting after S₀ is introduced). The surface integral is verified by means of variable separation of Laplace´s equation in bi-spherical coordinates.