Chapter 31, Problem 23PQ

A steady current I flows through a wire of radius a. The current density in a wire varies with r as J = kr², where k is a constant and r is the distance from the axis of the wire. Find expressions for the magnitudes of the magnetic field inside and outside the wire as a function of r. (Hint: Find the current through an Ampèrian loop of radius r using $I_{\text{thru}}={\displaystyle \int \stackrel{\to }{J}}\cdot d\stackrel{\to }{A}$.)