Past exam of the physics 2 paper of the University of Oxford / 2013 / 10 / ii / Solution

For a thin current-carrying cylindrical shell, a coaxial Amperian loop encloses zero current inside and the entire current outside. HenceMore generally $B(r)=0$ for $r<R$ and $B(r)={\mu }_0{I}_0/(2\pi r)$ for $r>R$. The tangential field discontinuity is supported by the surface current.