A Hertzian dipole is a short conducting wire carrying an approximately constant current ov...

A Hertzian dipole is a short conducting wire carrying an approximately constant current over its length l. If such a dipole is placed along the z-axis with its midpoint at the origin, and if the current flowing through it is i(t) = Io cos ωt. find the following:

(a) The retarded vector potential à (R. θ, ɸ) at an observation point Q(R. θ, ɸ) in a spherical coordinate system.

(b) The magnetic field phasoi

(R. θ, ɸ).

Assume I to be sufficiently small so that the observation point is approximately equidistant to all points on the dipole; that is. assume R' R.