Electromagnetism uniqueness theorem: Difference between revisions

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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 is not unique.

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

^ Smith, Glenn S. (1997-08-13). An Introduction to Classical Electromagnetic Radiation. Cambridge University Press. ISBN 9780521586986.

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[1] Smith, Glenn S. (1997-08-13). An Introduction to Classical Electromagnetic Radiation. Cambridge University Press. ISBN 9780521586986.

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 The '''electromagnetism uniqueness theorem''' states that providing [[Boundary condition|boundary conditions]] for [[Maxwell's equations]] uniquely fixes a solution for those equations.<ref>{{Cite book|url=https://books.google.ca/books?id=nZZu85Gq_D8C&pg=PA65&dq=electromagnetism+uniqueness+theorem&hl=en&sa=X&ved=0ahUKEwiL_cX6z_DVAhUM0oMKHeAtBmoQ6AEIKDAA#v=onepage&q=electromagnetism%20uniqueness%20theorem&f=false|title=An Introduction to Classical Electromagnetic Radiation|last=Smith|first=Glenn S.|date=1997-08-13|publisher=Cambridge University Press|isbn=9780521586986|language=en}}</ref>
+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 is not unique.
 ==See also==