General theory to determine the critical charge density

In this work we determine theoretically the critical charge density in a grounded metallic sphere system, uniformly charged dielectric plane, in the presence of grounded surfaces and in a general case. Special attention is paid to the influence of the system geometry in determining the most optimal conditions for obtaining the minimum critical charge density. This is a situation frequently encountered in industrial conditions and is important in evaluating the danger of electrostatic discharges.