On the Origin of the $\log d$ Variation of the Electrostatic Force Minimizing Voltage in Casimir Experiments

TL;DR

This paper explains the observed logarithmic variation of the minimizing voltage in Casimir experiments as a consequence of surface potential patches and geometric averaging within the Proximity Force Approximation.

Contribution

It provides a simple geometric model to account for the $ ext{log} hinspace d$ voltage variation observed in Casimir force measurements.

Findings

The voltage variation can be derived from surface patch effects.

The model aligns with experimental observations of the $ ext{log} hinspace d$ dependence.

Surface potential patches significantly influence electrostatic force measurements.

Abstract

A number of experimental measurements of the Casimir force have observed a logarithmic distance variation of the voltage that minimizes electrostatic force between the plates in a sphere-plane geometry. We show that this variation can be simply understood from a geometric averaging of surface potential patches together with the Proximity Force Approximation.