Earnshaw Theorem

one of the principal theorems of electrostatics, according to which a system of static point charges, located at a finite distance from one another, cannot be stable. It was formulated in the 1800’s by the British physicist and mathematician S. Earnshaw and follows from the fact that the potential energy of a static system of charges cannot have a minimum. The existence of such a potential energy minimum is a necessary condition for a system’s stable equilibrium.

The Earnshaw theorem played an important role in the development of atomic theory. It follows from the theorem that an atom cannot be constructed out of immobile charges that are bound to each other only by electrical forces and must be a dynamic rather than a static system.