THE INFLUENCE OF SURFACE-ROUGHNESS ON THE CAPACITANCE BETWEEN A SPHERE AND A PLANE

The problem of capacitance between a rough sphere and a rough plane ve ry close to each other is studied. The problem is simplified by gather ing the roughness of both members onto the plane. We begin by consider ing the case where the sphere and the plane are both ideally smooth. S tarting from a known exact formula of the capacitance involving an inf inite sum, we derive a simple and easy to use approximate expression. Then we consider the case where the sphere is smooth and the plane rou gh. The new formula for the capacitance involves an integral in which the weighting function is the height distribution. To validate this fo rmula, the results of two experiments, during which the derivative of the capacitance with respect to the separation has been recorded, are considered. Comparison of the measurements with theoretical calculatio ns indicates the approach is valid.