Unexplored aspects of a variational principle in electrostatics

TL;DR

This paper investigates a variational principle in electrostatics that uses the electric field magnitude to determine electric field lines, extending previous specific cases to a general context and exploring its implications.

Contribution

It validates and generalizes a variational principle involving electric field magnitude in electrostatics, beyond the specific grounded sphere problem.

Findings

The principle applies to general electrostatic configurations.

It offers a new method to determine electric field lines.

Potential implications for electrostatics problem-solving.

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.