Suppose f(r) is a localized vector function and j(r, t) = j(r|) exp(it) is a time-harmonic current

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Suppose f(r) is a localized vector function and j(r, t) = j(r|ω) exp(−iωt) is a time-harmonic current density where

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Prove that j(r, t) does not radiate and find the physical meaning of f(r, t).

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