Английская Википедия:Electromagnetism uniqueness theorem

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Шаблон:Short description The electromagnetism uniqueness theorem states the uniqueness (but not necessarily the existence) of a solution to Maxwell's equations, if the boundary conditions provided satisfy the following requirements:[1][2]

  1. At <math>t=0</math>, the initial values of all fields (Шаблон:Math, Шаблон:Math, Шаблон:Math and Шаблон:Math) everywhere (in the entire volume considered) is specified;
  2. For all times (of consideration), the component of either the electric field Шаблон:Math or the magnetic field Шаблон:Math tangential to the boundary surface (<math>\hat n \times \mathbf{E}</math> or <math>\hat n \times \mathbf{H}</math>, where <math>\hat n</math> is the normal vector at a point on the boundary surface) is specified.

Note that this theorem must not be misunderstood as that providing boundary conditions (or the field solution itself) 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.

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Шаблон:Electromagnetism-stub