Magnetic field — UPSC IFoS 2010 Physics PYQ

A long wire of radius a carries I amperes of current. The magnetic field surrounding it is given by H_\phi = \dfrac{I}{2\pi\rho} for \rho > a. Obtain expressions for (i) the magnetic energy stored per unit length in the region b \ge \rho \ge a and (ii) the equivalent inductance L per unit length.