Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

TL;DR

This paper investigates the sample-to-sample torque fluctuations between two randomly charged dielectric surfaces, revealing long-range behavior and potential experimental implications for detecting disorder effects beyond normal force measurements.

Contribution

It introduces the analysis of torque fluctuations caused by random charges, highlighting their long-range nature and significance compared to lateral forces in dielectric systems.

Findings

Sample-to-sample torque fluctuations scale with surface area.

Mean torque is zero, but fluctuations are long-range.

Torque fluctuations are more pronounced than lateral force effects.

Abstract

Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a central axle next to another randomly charged surface and show that although the resultant mean torque is zero, its sample-to-sample fluctuation exhibits a long-range behavior with the separation distance between the juxtaposed surfaces and that, in particular, its root-mean-square value scales with the total area of the surfaces. Therefore, the disorder-induced torque between two randomly charged surfaces is expected to be much more pronounced than the disorder-induced lateral force and may provide an effective way to determine possible disorder effects in experiments, in a manner that is independent of the usual normal force measurement.