A cylindrical wire of radius a is oriented with the z axis down its center line. The wire carries a nonuniform current down its length of density J = bρ a_z A/m² where b is a constant.

(a) What total current flows in the wire?

(b) Find H_in (0 < ρ < a), as a function of ρ;

(c) find H_out (ρ > a), as a function of ρ;

(d) verify your results of parts (b) and (c) by using∇ × H = J.