Past exam of the physics 2 paper of the University of Oxford / 2016 resit / 5

For a steady uniform current density in a nonmagnetic wire, the enclosed electric current at radius $r<a$ is $I_{\mathrm{enc}}=I{r}^2/a^2$. A circular Amperian loop and Ampère's law then giveThe magnetic field circles the wire according to the right-hand rule relative to the current direction. Its magnitude increases linearly from zero on the axis. The uniform-current assumption excludes skin effect.

Outside the wire, the Amperian loop encloses the entire electric current, soIts direction is again azimuthal, fixed by the right-hand rule. The inside and outside formulas join continuously at the maximum $B(a)={\mu }_{0}I/(2\pi a)$. The outer branch decays as $1/r$.