Scalar potential for charge distributions with ellipsoidal symmetry

Calculation of the electrostatic scalar potential in ellipsoidal coordinates is outlined. The ellipsoidal coordinate system is described, and the Laplace equation is discussed for this system. Special charge distributions having ellipsoidal symmetry, and therefore most easily treated in ellipsoidal coordinates, are assumed and their scalar potentials calculated, including the ellipsoidal shell, two-dimensional and three-dimensional Gaussian charge distribution, and two-dimensional uniform distribution. 2 refs