A long, straight wire with a circular cross section of radius $R$ carries a current $L$ . Assume that the current density is not constant across the cross section of the wire, but rather varies as $J=\alpha r,$ where $\alpha$ is a constant. (a) By the requirement that $J$ integrated over the cross section of the wire gives the total current $I,$ calculate the constant $\alpha$ in terms of $I$ and $R$ (b) Use Ampere's law to calculate the magnetic field $B(r)$ for (i) $r \leq R$ and (ii) $r \geq R$ . Express your answers in terms of $I$ .