Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 35

35 The current density \(\vec{J}\) inside a long, solid, cylindrical wire of radius \(a = 4.5 \text{ mm}\) is in the direction of the central axis, and its magnitude varies linearly with radial distance \(r\) from the axis according to \(J = J_0 r / a\), where \(J_0 = 420 \text{ A/m}^2\). Find the magnitude of the magnetic field at (a) \(r = 0\), (b) \(r = a/2\), and (c) \(r = a\).