Electrostatic interaction energy between the electrodes of a concentric coplanar sensor

Abstract

The capacitive testing method using coplanar capacitive sensors represents a relatively new technique for non-destructive evaluation of the properties of a given material. The most conventional design of a coplanar capacitive sensor is that of two oppositely charged coplanar electrodes located at some separation distance from each other. The electrodes can have any shape including designs with circular symmetry. The concentric coplanar sensor is a special case of a device with circular symmetry. It comprises a disk as the inner electrode and an annulus as the outer one. In this work we analyze the features of the electrostatic interaction energy between the two electrodes of a concentric coplanar sensor by considering a model consisting of a uniformly charged disk and a uniformly charged annulus that is concentric and coplanar to the disk. For the sake of generality, we assume that the two objects carry an arbitrary amount of net charge and their dimensions are arbitrary. We obtain an exact expression for the electrostatic interaction energy of the system as a function of three important length scales, radius of disk and inner/outer radii of the annulus. The interplay between these parameters determines the features of the electrostatic interaction energy between the electrodes as well as the overall performance of the sensor.