Suppose the (electrically neutral) yz plane carries a time-dependent but uniform surface...

Suppose the (electrically neutral) yz plane carries a time-dependent but uniform surface current

(a) Find the electric and magnetic fields at a height x above the plane if

(i) a constant current is turned on at t = 0:

(ii) a linearly increasing current is turned on at t = 0:

(b) Show that the retarded vector potential can be written in the form

and from this determine E and B.

(c) Show that the total power radiated per unit area of surface is

Explain what you mean by “radiation,” in this case, given that the source is not localized.²²