A very long (infinite) wire with a very small cross sectional area A is coincident with the z-axis. The wire carries a current I (t) = I exp(−iωt).
(a) Use the Poynting vector to determine the dependence of the radiation fields on the variable ρ (cylindrical coordinates) which measures the distance perpendicular to the wire.
(b) The radiation magnetic field from a time-dependent point electric dipole p(t ) at the origin is

Explain why the radiation magnetic field from the wire can be regarded as a superposition of fields like the one above.
(c) Carry out the superposition and confirm the answer you got in part (a). Simplify the integral you get by assuming that z

cBrad(r, t) = Hof dp(t-r/c) dt 4 r X