Electromagnetism uniqueness theorem

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

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

• Maxwell's equations
• Green's function
• Uniqueness theorem

References

• L.D. Landau, E.M. Lifshitz (1975). The Classical Theory of Fields. Vol. Vol. 2 (4th ed.). Butterworth–Heinemann. ISBN 978-0-7506-2768-9. {{cite book}}: |volume= has extra text (help)
• J. D. Jackson (1998). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 978-0-471-30932-1.

Specific