Biot-Savart Law & Circular Coils question from NEET 2019

Answer: (b)

1. The current splits into a $\frac{3}{4}$ arc and a $\frac{1}{4}$ arc; currents are inversely proportional to length: $i_1 = \dfrac{i}{4}$, $i_2 = \dfrac{3i}{4}$.
2. Field of an arc $\propto I\theta$: $\dfrac{i}{4}\cdot\dfrac{3\pi}{2} = \dfrac{3i}{4}\cdot\dfrac{\pi}{2}$, and the two arcs give opposite directions at P, so they cancel.
3. Both straight wires point along lines through P, so they give zero field at P.
4. So the answer is (b) zero.