  We present approximate methods for calculating the three-dimensional electric
potentials of finite surface electrodes including gaps between electrodes, and
estimate the effects of finite electrode thickness and an underlying dielectric
substrate. As an example we optimize a radio-frequency surface-electrode ring
ion trap, and find that each of these factors reduces the trapping secular
frequencies by less than 5% in realistic situations. This small magnitude
validates the usual assumption of neglecting the influences of gaps between
electrodes and finite electrode extent.
