Unexplored aspects of a variational principle in electrostatics

Abstract

The electrostatic field magnitude can play a role in a variational principle similar to the role of the index of refraction in geometrical optics, allowing the determination of the electric field lines. This was identified in the context of the grounded conducting sphere image problem. Assuming the knowledge of the magnitude of the electric field, in this paper we validate this principle for the general case and explore some of its consequences.