Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2010 / Paper 1 / Section A / 3

Apply Ampère's law on a concentric circle. Uniform current density is $J=I/(\pi a^2)$, so the enclosed current is $I{r}^2/a^2$ inside and $I$ outside. With permeability ${\mu }_0$,The field circulates azimuthally by the right-hand rule. Its magnitude rises linearly from zero, is continuous and maximal at the surface, then falls as $1/r$. End effects are neglected.