Forces and force gradients due to patch fields and contact-potential differences

Abstract

We derive expressions for the forces and force gradients which exist between infinite parallel metallic surfaces in terms of the spatial distributions of the surface potentials. The main motivation for this is to enable the forces and force gradients to be calculated from electrical measurements of the surface potentials. However, by making some worst-case assumptions about the potential distributions, we establish a limit for the relative displacement of the spacecraft and proof mass in the LISA mission of