A family of repulsive neutral conductor geometries via abstract vector spaces

TL;DR

This paper demonstrates that specific geometries of neutral conductors can repel point charges or dipoles, using abstract vector space methods, and identifies families of shapes capable of Casimir repulsion.

Contribution

It introduces a general vector space framework to prove the existence of neutral conductor geometries that repel charges and dipoles, expanding understanding of electromagnetic boundary effects.

Findings

Certain neutral conductor shapes can repel point charges.

Specific geometries can induce Casimir repulsion.

The approach uses abstract vector space properties for proofs.

Abstract

Recently it was shown that it is possible for a neutral, isolated conductor to repel a point charge (or, a point dipole). Here we prove this fact using general properties of vectors and operators in an inner-product space. We find that a family of neutral, isolated conducting surface geometries, whose shape lies somewhere between a hemispherical bowl and an ovoid, will repel a point charge. In addition, we find another family of surfaces (with a different shape) that will repel a point dipole. The latter geometry can lead to Casimir repulsion.