Surface Contact Potential Patches and Casimir Force Measurements

TL;DR

This paper analyzes contact potential patches' effects on Casimir force measurements, showing they do not impact electrostatic calibration but can cause residual forces that affect measurement accuracy, explained through models and simple capacitor analogies.

Contribution

It provides simplified calculations of patch effects, demonstrating their minimal impact on calibration but potential to cause residual forces that influence Casimir measurement accuracy.

Findings

Patch potentials do not affect electrostatic calibration due to Laplace's equation linearity.

Residual electrostatic forces persist even at force-minimizing voltages.

The residual force varies with distance and can be modeled by a simple two-parameter function.

Abstract

We present calculations of contact potential surface patch effects that simplify previous treatments. It is shown that, because of the linearity of Laplace's equation, the presence of patch potentials does not affect an electrostatic calibration (of force and/or distance) of a two-plate Casimir measurement apparatus. Using models that include long-range variations in the contact potential across the plate surfaces, a number of experimental observations can be reproduced and explained. For these models, numerical calculations show that if a voltage is applied between the plates which minimizes the force, a residual electrostatic force persists, and that the minimizing potential varies with distance. The residual force can be described by a fit to a simple two-parameter function involving the minimizing potential and its variation with distance. We show the origin of this residual force by use of a simple parallel capacitor model. Finally, the implications of a residual force that varies in a manner different from 1/d on the accuracy of previous Casimir measurements is discussed.