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.