Because an irrotational vector field has a scalar potential and a solenoidal vector field has a vector potential, the Helmholtz decomposition states that a vector field ( satisfying appropriate smoothness and decay conditions ) can be decomposed as the sum of the form-\ operatorname { grad } \ Phi + \ operatorname { curl } \ mathbf { A } where is a scalar field, called scalar potential, and is a vector field called a vector potential.
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