Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 68

A circular rod of magnetic material with permeability is inserted coaxially in a very long air solenoid. The radius of the rod, a, is less than the inner radius, b, of the solenoid. The solenoid's winding has n turns per unit length and carries a current I.
a) Find the values of B, H, and M inside the solenoid for r and for a
b) What are the equivalent magnetization current densities J mv and J ms for the magnetized rod