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.

We derive a system of integral equations for the surface charge distribution on the electrodes of a parallel-plate capacitor for which the profile of one electrode is rough. We show that the solution to this system of equations is tractable using a perturbation technique assuming small surface heights compared with the mean plate separation. The accuracies of the first- and second-order perturbative approximations and of the local height approximation are evaluated for a few examples with a one-dimensional rough surface by comparing them with exact numerical results obtained by solving the boundary integral equations directly using a numerical procedure. Some general guidelines for when the first- and second-order approximations will be accurate are given. It is shown that the perturbative formulation provides approximations with a regime of validity that may extend over a larger region than the regime of validity of the local height approximation. These results could be useful for capacitive-sensor design purposes or in modelling solid-state electronic devices.

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An experimental and theoretical investigation of the temporal spread of an ultrashort light pulse on transmission through a highly scattering medium has been made. For the strongly diffuse light, the transmitted pulse may be described by a universal function whose duration can be directly related to the width of the sample. For sufficiently scattering samples, experimental data and the diffusion approximation indicate that the output pulse duration scales with the square root of the sample width.