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 centers of the circle and square respectively, then the ratio \( \frac{\mathrm{B}_{\mathrm{A}}}{\mathrm{B}_{\mathrm{B}}} \) is:

A \( \frac{\pi^{2}}{16 \sqrt{2}} \)

B \( \frac{\pi^{2}}{16} \)

C \( \frac{\pi^{2}}{8 \sqrt{2}} \)