The current density in a wire of radius a varies with radial distance r as

$J=k{r}^2$ , where k is a constant.

dI = JdA

$\Rightarrow dI=k{r}^2\left(2\pi rdr\right)$

$\Rightarrow I=2\pi k{\displaystyle \underset{0}{\overset{a}{\int }}{r}^{3}dr}$    $\Rightarrow I=\frac{1}{2}\pi k{a}^4$

Further, field for r > a is

$B=\frac{{\mu }_{0}I}{2\pi r}=\frac{{\mu }_{0}k{a}^4}{4r}$

And field for r < a is

$B=\frac{{\mu }_0\left(\frac{\pi k{r}^4}{2}\right)}{2\pi r}=\frac{1}{4}{\mu }_{0}k{r}^3$