Electromagnetism uniqueness theorem

The electromagnetism uniqueness theorem states that providing boundary conditions for Maxwell's equations uniquely fixes a solution for those equations.[1]

However, this theorem must not be misunderstood as that providing boundary conditions (or the field solution itself) uniquely fixes a source distribution. One counterexample 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.

See also

References
  • L.D. Landau, E.M. Lifshitz (1975). The Classical Theory of Fields. Vol. 2 (4th ed.). Butterworth–Heinemann. ISBN 978-0-7506-2768-9.
  • J. D. Jackson (1998). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 978-0-471-30932-1.
Specific
  1. Smith, Glenn S. (1997-08-13). An Introduction to Classical Electromagnetic Radiation. Cambridge University Press. ISBN 9780521586986.
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