2023/08/22 by Dukes, Julian J., Shotwell, Brian
#Classical Physics (physics.class-ph) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2308.11697
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.