Calibration of the electrostatic force between spheres at constant potential

A Kelvin-type apparatus was used to measure the electrostatic force exerted between spheres held at constant potential. We found the electrostatic force to be attractive, neutral, or repulsive depending upon differences in magnitude of the applied potentials. A calibration of the electrostatic interaction force between two spheres, using Coulombic force (action-at-a-distance) complemented with Gauss' potential gives results that are exact within experimental error. The practical importance of an exact calibration of the electrostatic contribution to the interaction force is that absolute measurements appears to be possible. Because the exact solution to the interaction force is available suggests that test surfaces in atomic force and surface force apparatus used to probe interfacial forces at small separation distances at the A scale should have a sphere-sphere geometry.