Calculation of the electric field and the capacitance of a charged spherical bowl by means of toroidal co-ordinates

Mathematical expressions for the potential function and the electric capacitance of a charged spherical bowl with respect to infinity are derived. Some numerical calculations of the potential field are presented for a charged spherical bowl of different openings and for the limiting case of a circular disc to illustrate the derived results. The mathematical expressions derived for the charged density on the concave and the convex sides of the spherical bowl are identical to those given by Kelvin, who employed the method of inversion.