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 $\large\frac{B_A}{B_B}$ is :

Question

$\begin{array}{1 1} (1) \large\frac{\pi^2}{8} \\ (2) \large\frac{\pi^2}{16 \sqrt 2} \\ (3) \large\frac{\pi^2}{16} \\ (4) \large\frac{\pi^2}{8 \sqrt 2} \end{array} $