Let a spherical bowl have diameter d, let a be the distance from the bottom to a lip, and let r be the distance from the bottom to a point on the bowl. If the bowl is placed at a voltage V, then the surface charge density on the outside surface is
and the outside surface has a surface charge density
References
Jeans, J. H. The Mathematical Theory of Electricity and Magnetism, 5th ed. Cambridge, England: Cambridge University Press, p. 250, 1963.
