A current loop $ABCD$ is held fixed on the plane of the paper. 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. Angle made by $AB$ and $CD$ at the origin $O$ is $30^{\circ }$. The magnitude of the magnetic field ($B$) due to loop $ABCD$ at the origin ($O$) is:

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