Abstract :
The problem of calculating the electric field in a sphere-gap, usually attacked by means of an infinite series of image charges, is here approached through the direct solution of Laplace´s equation. This solution is obtained in dipolar co-ordinates, which are suitable for problems in which boundary conditions are specified on two nonintersecting spherical surfaces. The result is given as an infinite series, from which is derived a curve, universally applicable, for the maximum voltage gradient in the field between two equal spheres. The alternative method of solution by image charges is briefly outlined for comparison.
