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arXiv · 2308.11697

A family of repulsive neutral conductor geometries via abstract vector spaces

Julian J. Dukes·Brian Shotwell
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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.

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Julian J. Dukes, Brian Shotwell. 2023-08-22. A family of repulsive neutral conductor geometries via abstract vector spaces. https://arxiv.org/abs/2308.11697

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