$A$ current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $= a$) of the loop are joined by two straight wires $AB$ and $CD$. $A$ steady current $I$ is flowing in the loop. The angle made by $AB$ and $CD$ at the origin $O$ is $30^\circ$. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is:

• A
  $0$
• B
  $\frac{{\mu _0}I(b - a)}{{24ab}}$
• C
  $\frac{{\mu _0}I}{{4\pi }}\left[ {\frac{{b - a}}{{ab}}} \right]$
• D
  $\frac{{\mu _0}I}{{4\pi }}\left[ {2(b - a) + \frac{{\pi (a + b)}}{3}} \right]$