Limits on the accuracy of isoelectronic gravity measurements at short separation due to patch potentials

In force sensing experiments intended to measure non-Newtonian gravitational signals electrostatic patch potentials can give rise to spurious forces, torques, and noise. Undesired patch-induced interactions can lead to systematic effects which limit accuracy, and noise can place lower limits on precision. In this paper we develop the theory for electrostatic patch effects on isoelectronic experiments, where their mean effect is nullified by design. We derive analytical expressions for the patch force and torque power spectrum to estimate the limitations introduced by patch-induced signals.