A random walk related to the capacitance of the circular plate condenser

Abstract

It is shown that the solution of Love’s equation for the capacitance of the circular plate condenser can be expressed in terms of the mean duration of a certain one-dimensional random walk with absorbing barriers. The interpretation as a random walk makes it possible to confirm the fact that the actual capacitance of the condenser is always larger than the value given by the standard approximation for small separations, and yields an upper bound as well. In addition to its theoretical interest, the random walk appears to provide a practical means for the calculation of the capacitance by a Monte Carlo technique.