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The uniqueness theorem states that a solution of Laplace's equation satisfying the given boundary conditions is

  • A.the only such solution
  • B.one of infinitely many, all physically equivalent
  • C.unique only if the region is bounded and simply connected
  • D.unique only if the boundary is a conductor throughout

Answer: A

This is what makes guessing a solution a legitimate method: if a function satisfies the equation and matches the boundaries, it must be the answer, however it was arrived at. The method of images rests entirely on this licence.

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