On the evaluation of the capacitance of toroidal capacitors with a moon-shape meridian cross section

The toroidal capacitors studied in this paper consist of electrodes with meridian cross sections that are circular arcs meeting at the axis, and separated from each other by two small insulating spheres at their meeting points. The description and analysis of such capacitors is carried out by using bi spherical coordinates. The R-separability of the Laplace equation in these coordinates requires the use of the Green function technique, just like in the related problems of toroidal, spherical-cap-electrode, and bi spherical capacitors (1-3). An overall comparison of the solutions of the four problems is specially instructive. (Author)