The fundamental theorem of vector analysis states that any vector field meeting certain conditions (of decaying towards infinity) can be resolved into irrotational and solenoidal component vector fields.
This implies that any vector field E meeting certain decay criteria can be considered to be generated by a pair of potentials: a scalar potential φ and a vector potential A. Then the negative gradient of the scalar potential is equated with the irrotational component, and the curl of the vector potential is equated with the solenoidal component:
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