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The magnitude of the magnetic field (B) due to the loop

Question:

The magnitude of the magnetic field (B) due to the loop $A B C D$ at the origin $(O)$ is :-

A current loop $\mathrm{ABCD}$ is held fixed on the plane of the paper as shown in the figure. The arcs $\mathrm{BC}$ (radius $=b$ ) and DA (radius $=$ a) of the loop are joined by two straight wires AB and CD. A steady current $\mathrm{I}$ is flowing in the loop. Angle made by $\mathrm{AB}$ and $\mathrm{CD}$ at the origin $\mathrm{O}$ is $30^{\circ}$. Another straight thin wire with steady current $\mathrm{I}_{1}$ flowing out of the plane of the paper is kept at the origin.

1. $\frac{\mu_{0} \mathrm{I}}{4 \pi}\left[\frac{\mathrm{b}-\mathrm{a}}{\mathrm{ab}}\right]$

2. $\frac{\mu_{0} \mathrm{I}}{4 \pi}\left[2(b-a)+\frac{\pi}{3}(a+b)\right]$

3. Zero

4. $\frac{\mu_{0} \mathrm{I}(\mathrm{b}-\mathrm{a})}{24 \mathrm{ab}}$

Correct Option: , 4

Solution: