Production of uniform electrostatic fields by a slotted conducting spherical shell

A spherical structure that specifies electric potential on a spherical surface to produce a uniform electric field near the center of the sphere is considered. The surface is divided on lines of constant latitude (polar angle), and the resulting bands are constrained to have particular voltages. The particular case of three conducting surfaces with voltages V₁, 0, and -V₁ is considered in detail. Polar angles are determined that give the required uniformity of the field