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 Ck and 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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