(Solution) - Suppose This is incidentally the simplest possible spherical -(2025 Original AI-Free Solution)

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Suppose (This is, incidentally, the simplest possible spherical wave. For notational convenience, let (kr ? wt) ? u in your calculations.)
(a) Show that E obeys all four of Maxwell's equations, in vacuum, and find the associated magnetic field.
(b) Calculate the Poynting vector. Average S over a full cycle to get the intensity vector I. (Does it point in the expected direction? Does it fall off like r?2, as it should?)
(c) Integrate I ? da over a spherical surface to determine the total power radiated.