Past exam of the mathematics course of the University of Cambridge / 2009 / ib / Paper 3 / 17A / a / Solution

Choose $+z$ along the current in the inner conductor. Cylindrical symmetry and Ampère's law give $2\pi r{B}_{\varphi }={\mu }_{0}I$ for $a<r<b$, soThe opposite current on the outer shell makes the net enclosed current zero outside both conductors; the long-cylinder approximation neglects end fields.