Consider a cylindrical conductor with a hole bored along its central axis, inner radius a $=2\mathrm{.}0$ cm $,$ outer radius $b=4\mathrm{.}0cm.$ The current density is given by $J=c{r}^2$ where $c=3\mathrm{.}0{10}^6\frac{A}{m^4}.$

$($a$)$ Find using Ampere's law the magnetic field symbolically a distance $r$ from the central axis.

$($b$)$ Evaluate this numerically at the point $r=3cm$ from the central axis.