Theorem in electromagnetism says if the divergence [itex]\nabla\cdot E[/itex] and the curl [itex]\nabla\times E[/itex] are known, then E is uniquely determined. So my question is, the divergence equation gives 1 constraint and the curl equation gives 3 constraints, which add up to 4 constraints. On the other hand, the electric filed E has only 3 unknown components. Does it mean 4 equations are overdetermined and thus has dependency?
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