Distortion of electric field homogeneity between two thin toroidal electrodes by a dielectric sphere

We assess the influence of a radius and a relative permittivity of an isotropic dielectric sphere on electric field homogeneity. The homogenous electric field is generated using two thin toroidal electrodes, charged by equal charges of opposite signs. The Poisson equation is solved by a method of separation of variables. Increase in a relative permittivity of the sphere and in its radius, produces more distortions of the electric field homogeneity.