 Abrupt line-current wavefront singularity

The ideal fields after instantaneous switching behave as $E_z,H_{\varphi }\propto (t-r/c{)}^{-1/2}$ near arrival, and the radial Poynting vector as $(t-r/c{)}^{-1}$. A finite switching rise time smooths the ideal front; the singular solution does not represent a finite-energy real pulse.