Magnetic Field of Straight Wires question from JEE Main 2023 (1 Feb, Shift 1)

Answer: (a)

1. The lower vertical wire lies on a line through P, so it gives zero field.
2. Upper semi-infinite wire ending above P: $\frac{\mu_0 i}{4\pi r}$, out of the page.
3. Semicircle (anticlockwise): $\frac{\mu_0 i}{4r}$, out of the page.
4. $B = \frac{\mu_0 i}{4r} + \frac{\mu_0 i}{4\pi r} = \frac{\mu_0 i}{2r}\left(\frac{1}{2} + \frac{1}{2\pi}\right)$
5. So the answer is (a).