Rough-surface capacitor: approximations of the capacitance with elementaryfunctions

We consider the electrical capacitance of a parallel-plate capacitor with o ne rough electrode. The roughness is characterized by its amplitude and its wavenumber scale; the capacitance depends on both of these variables as we ll as the form of the roughness. We calculate the capacitance in the four l imit cases of the two variables mentioned above. On the basis of these limi t cases, we approximate the capacitance with elementary functions for the c ase of any surface roughness. We compare the capacitances calculated in thi s approach with precise numerical solutions for different forms of roughnes s.