Magnetic Field of Straight Wires question from JEE Main 2025 (28 Jan, Shift 2)

Answer: (b)

1. The right wire lies on a line through O, so it gives zero field.
2. Lower semi-infinite wire, ending at the foot of the perpendicular from O: $\frac{\mu_0 I}{4\pi a}$, into the page.
3. Three-quarter arc (clockwise): $\frac{3}{4}\cdot\frac{\mu_0 I}{2a} = \frac{\mu_0 I}{4\pi a}\cdot\frac{3\pi}{2}$, into the page.
4. $B = \frac{\mu_0}{4\pi}\frac{I}{a}\left[\frac{3\pi}{2} + 1\right]$
5. So the answer is (b).