Simulating the electrostatic patch force in sphere-plate and plate-plate geometries

Potential patches are responsible for a force between closely-spaced objects that forms a parasitic contribution to sensitive force measurements. Existing analytical models cannot account for the patch force in the 3D geometries of real experiments. Here, we present a finite-element method model to evaluate the impact of patches in arbitrary geometries. First, we test our model against the plate-plate and sphere-plate geometries, for which the exact solutions are known. Then, we apply it to the analytically unwieldy case of plate-concave plate that is relevant for Casimir force measurements. This work provides a reliable estimation of the parasitic contribution from random potential patches.