Question: A vector function Z(r) satisfies Z = 0 and Z = 0 everywhere in a simply-connected volume V bounded by a surface

A vector function Z(r) satisfies ∇ · Z = 0 and ∇ ×Z = 0 everywhere in a simply-connected volume V bounded by a surface S. Modify the proof of the Helmholtz theorem in the text and show that Z(r) can be found everywhere in V if its value is specified at every point
on S.

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