Magnetic Field of Straight Wires question from JEE Main 2023 (25 Jan, Shift 1)

Answer: (c)

1. Use: semi-infinite wire ending at the foot gives $\frac{\mu_0 I}{4\pi r}$, an infinite wire gives $\frac{\mu_0 I}{2\pi r}$, a semicircle gives $\frac{\mu_0 I}{4r}$, a full loop gives $\frac{\mu_0 I}{2r}$; a wire whose line passes through O gives zero.
2. Full loop with infinite wire opposing: $\frac{\mu_0 I}{2r} - \frac{\mu_0 I}{2\pi r} = \frac{\mu_0 I}{2\pi r}[\pi - 1]$ (III).
3. Semicircle with two semi-infinite wires adding (hairpin): $\frac{\mu_0 I}{4\pi r}[\pi + 2]$ (I).
4. Semicircle with one semi-infinite wire adding: $\frac{\mu_0 I}{4\pi r}[\pi + 1]$ (IV); semicircle with both wires through O: $\frac{\mu_0 I}{4r}$ (II).
5. So the answer is (c) A-III, B-I, C-IV, D-II.