The Cartesian components of the electric field in a charge-free region of space are E k =

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The Cartesian components of the electric field in a charge-free region of space are Ek = Ck + Djkrj, where Cand Djk are constants.

(a) Prove that Djk is symmetric (Djk = Dkj) and traceless (∑k Dkk = 0).

(b) Find the most general electrostatic potential that generates the electric field in part (a).

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