 Switched infinite-wire retarded potential

For a spatially uniform line current $I\Theta (t)$, the causal potential outside the line is $A_z=({\mu }_{0}I/2\pi )\mathrm{arcosh}(ct/r)$ for $ct>r$, and zero before arrival. The finite causal integration length makes it finite at finite time, unlike an absolute magnetostatic potential for an infinite wire.