The electrostatic capacity of an object is defined by the following problem. Assume the object is conducting and charged so that the surface has a constant (unit) potential, and the potential outside the object decays to zero at infinite distance. The capacity can then be defined in terms of the asymptotic decay at large distances of the solution to Laplace's equation in the space surrounding the object [40,41,42]. Units are chosen such that a sphere of radius R has a capacitance C = R [51]. The problem of the capacitance of an ellipsoid of revolution has also been solved [52]. Normalized by the capacitance of a sphere with equal volume, the capacitance of an ellipsoid of revolution equals
where the aspect ratio x = a/b. Hubbard and Douglas [51] have recently shown that the Stokes friction of a Brownian particle is proportional to C to a very good approximation, and that capacity is related to many physical processes and properties relating to the origin of Laplace's equation in describing heat, electrical, and fluid flow [40,41,42]. This relation between the translational friction and capacity is exact for ellipsoids [51]. It is rigorously known that C is a minimum for a sphere for all objects having a finite volume [40].