Electromagnetism Uniqueness Theorem

The electromagnetism uniqueness theorem states that a solution to Maxwell's equations, if one exists, is unique once suitable boundary conditions are fixed: the initial values of the electric, magnetic, and associated field quantities must be specified everywhere in the volume at the starting time, and thereafter either the tangential electric field or the tangential magnetic field must be specified at the boundary for all later times. The theorem guarantees only that the fields inside the specified volume are unique, not that the sources producing a given external field are unique, since a uniformly charged sphere, for example, produces the same external field as a point charge of the same total charge placed at its center.