A long, solid, conducting cylindrical wire having radius consists of a current density J(r) = Cr and carries a net current I.
i) Determine an expression for the constant C in terms of I and a.
ii) Determine the magnetic field B(r) within the wire, that is, for 0 < r < a.
iii) Determine the magnetic field B(r) outside the wire, that is, for r > a.