Uniform current is flowing. Current enclosed in the first amperean path is,

 $\frac{\mathit{\text{I}}·\pi {\mathit{\text{r}}}_1^2}{\pi {\mathit{\text{R}}}^2}=\frac{\mathit{\text{I}}{\mathit{\text{r}}}_1^2}{{\mathit{\text{R}}}^2}$
$\therefore$   B = $\frac{{\mu }_0\times \text{current}}{\text{path}}=\frac{{\mu }_0·\mathit{\text{I}}{\mathit{\text{r}}}_1^2}{2\pi {\mathit{\text{r}}}_1{\mathit{\text{R}}}^2}=\frac{{\mu }_0\mathit{\text{I}}{\mathit{\text{r}}}_1}{\text{2}\pi {\mathit{\text{R}}}^2}$
Magnetic induction at a distance,

${\mathit{\text{r}}}_2=\frac{{\mu }_0·\mathit{\text{I}}}{2\pi {\mathit{\text{r}}}_2}$
$\therefore$   $\frac{{\mathit{\text{B}}}_1}{{\mathit{\text{B}}}_2}=\frac{{\mathit{\text{r}}}_1{\mathit{\text{r}}}_2}{{\mathit{\text{R}}}^2}=\frac{\frac{\mathit{\text{a}}}{2}·2a}{a^2}$   =  1.