Chapter 14, Problem 76AP

Suppose that a cylindrical solenoid is wrapped around a core of iron whose magnetic susceptibility is x. Using Equation 14.9, show that the self-inductance of the solenoid is given by $L=\frac{(l+x)+{\mu }_0{n}^{2}A}{l}$ where l is its length, A its cross-sectional area and N its total number of turns. $N{\Phi }_m=\text{U}$