On the Casimir repulsion in sphere-plate geometry

TL;DR

This paper investigates the Casimir force between a sphere and a plane, focusing on conditions that lead to repulsion due to magnetic permeability effects, with numerical estimates and asymptotic analysis.

Contribution

It provides the first detailed analysis of Casimir repulsion in sphere-plate systems considering magnetic permeability, including numerical estimates and asymptotic behaviors.

Findings

Numerical estimates for vacuum energy with a perfectly permeable sphere.

Asymptotic expressions for repulsive force at short and long distances.

Discussion of conditions constraining Casimir repulsion.

Abstract

The electromagnetic vacuum energy is considered in the presence of a perfectly conducting plane and a ball with dielectric permittivity $\varepsilon$ and magnetic permeability $\mu$, $\mu\ne1$. The attention is focused on the Casimir repulsion in this system caused by magnetic permeability of the sphere. In the case of perfectly permeable sphere, $\mu=\infty$, the vacuum energy is estimated numerically. The short and long distance asymptotes corresponding to the repulsive force and respective low temperature corrections and high temperature limits are found for a wide range of $\mu$. The constraints on the Casimir repulsion in this system are discussed.