Suppose (This is, incidentally, the simplest possible spherical wave. For notat...

Suppose

(This is, incidentally, the simplest possible spherical wave. For notational convenience, let (kr − ωt) ≡ 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.