Rough-surface capacitor: approximations of the capacitance with elementary functions

Abstract

We consider the electrical capacitance of a parallel-plate capacitor with one rough electrode. The roughness is characterized by its amplitude and its wavenumber scale; the capacitance depends on both of these variables as well as the form of the roughness. We calculate the capacitance in the four limit cases of the two variables mentioned above. On the basis of these limit cases, we approximate the capacitance with elementary functions for the case of any surface roughness. We compare the capacitances calculated in this approach with precise numerical solutions for different forms of roughness.