Magnetic Field of Straight Wires question from MHT CET 2025 (20 Apr, Shift 2)

Answer: (b)

1. PQ lies on a line through O: zero field.
2. Arc QRS is $\frac{3}{4}$ of a circle: $\frac{3}{4} \cdot \frac{\mu_0 i}{2r} = \frac{\mu_0 i}{4\pi r} \cdot \frac{3\pi}{2}$, anticlockwise, so along $+\hat{k}$.
3. ST is semi-infinite starting directly below O: $\frac{\mu_0 i}{4\pi r}$, also along $+\hat{k}$.
4. $\vec{B} = \frac{\mu_0 i}{4\pi r}\left(\frac{3\pi}{2} + 1\right)\hat{k}$, so the answer is (b).