magnetic field outside the conductor

Question

I think B option should be correct .
As by using amphere circuital law , consider a loop of radius r .
$B(2\pi r)=\mu i$
i we have calculated in option A.

Comments

Please show your calculation.

Answer 1

Outside of the conductor, the magnetic field at radius $r$ is given by Ampere's Circuit Law :
$B(2\pi r)=\mu_0 I=\mu_0 (\frac13 J_0 \pi a^2)$
in which I have used the result from (A). Therefore
$B=\mu_0 J_0 \frac{a^2}{6r}$
so answer (B) is not correct.