Electromagnetism uniqueness theorem


The electromagnetism uniqueness theorem states the uniqueness of a solution to Maxwell's equations, if the boundary conditions provided satisfy the following requirements:
  1. At, the initial values of all fields everywhere is specified;
  2. For all times, the component of either the electric field or the magnetic field tangential to the boundary surface is specified.
Note that this theorem must not be misunderstood as that providing boundary conditions uniquely fixes a source distribution, when the source distribution is outside of the volume specified in the initial condition. One example is that the field outside a uniformly charged sphere may also be produced by a point charge placed at the center of the sphere instead, i.e. the source needed to produce such field at a boundary outside the sphere is not unique.