Chapter 1: Vector AnalysisThe Helmholtz Theorem

• Consider the vector function F(r):

  • Assume that the divergence of F(r) is D(r)
  • Assume that the curl of F(r) is C(r)

• If both D(r) and C(r) are going to zero faster than 1/r2 when r approaches infinity than F(r) is uniquely defined:

where

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