Statement of The Theorem
Let F be a vector field on a bounded domain V in R3, which is twice continuously differentiable. Then F can be decomposed into a curl-free component and a divergence-free component:
where
If V is R3 itself (unbounded), and F vanishes sufficiently fast at infinity, then the second component of both scalar and vector potential are zero. That is,
Read more about this topic: Helmholtz Decomposition
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