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 $B_{\mathrm{A}}$ and $B_{\mathrm{B}}$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_{\mathrm{A}}}{B_{\mathrm{B}}}$ is

• A

  $\frac{{\mathrm{\pi }}^2}{16}$
• Correct answer
  B

  $\frac{{\mathrm{\pi }}^2}{8\sqrt{2}}$
• C

  $\frac{{\mathrm{\pi }}^2}{8}$
• D

  $\frac{{\mathrm{\pi }}^2}{16\sqrt{2}}$

Hence, the correct answer is option: 'B'.