Two identical wires A and B, each of length $‘l’$, carry the same current $I$. Wire A is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $‘a’$. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is :

Question

( A ) $\frac{\pi^2}{16}$
( B ) $\frac{\pi^2}{8\sqrt{2}}$
( C ) $\frac{\pi^2}{16 \sqrt{2}}$
( D ) $\frac{\pi^2}{8}$