Comment on Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry

Recently Kim [Phys. Rev. A 78, 020101(R) (2008)] performed electrostatic calibrations for a plane plate above a centimeter-size spherical lens at separations down to 20-30 nm and observed anomalous behavior. It was found that the gradient of the electrostatic force does not depend on separation as predicted on the basis of a pure Coulomb contribution. Some hypotheses which could potentially explain the deviation from the expected behavior were considered, and qualitative arguments in favor of the influence of patch surface potentials were presented. We demonstrate that for the large lenses at separations of a few tens of nanometers from the plate, the electrostatic force law used by the authors is not applicable due to possible deviations of the mechanically polished and ground lens surface from a perfect spherical shape. A model is proposed which provides a possible explanation for the observed anomalous behavior using the standard Coulomb force.