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Consider the vector field ʊ(r) = (x² + y²)êx + (x² + y²)êy + z²êz. Decompose the vector
field (r) into the sum of two other vector fields, a (r) and 5(r), such that a(r) has no
divergence (it is solenoidal) and 5 (r) has no curl (it is irrotational). The answer is not
unique. This is the Helmholtz decomposition.

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