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

Unexplored aspects of a variational principle in electrostatics