Chapter 6, Problem 27P

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) = I₀ cos ωt, find the following:

1. (a) The retarded vector potential $\tilde{A}\text{(}R\text{,}\theta \text{,}\varphi \text{)}$ at an observation point Q(R, θ, φ) in a spherical coordinate system.
2. (b) The magnetic field phasor $\tilde{H}\text{(}R\text{,}\theta \text{,}\varphi \text{)}$.

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