Q 12-04-136JEE MainJEE Main 2023 (1 Feb, Shift 1)Medium
Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires.
Answer: (C) $\dfrac{\mu_0i}{2r}\left(\dfrac12+\dfrac1{2\pi}\right)$
- Semicircle: $\dfrac{\mu_0i}{4r}$.
- Horizontal semi-infinite wire ending directly above $P$ at distance $r$: $\dfrac{\mu_0i}{4\pi r}$, in the same sense.
- Vertical wire: lies along a line through $P$, so it gives nothing.
$$B=\frac{\mu_0i}{4r}+\frac{\mu_0i}{4\pi r}=\frac{\mu_0i}{2r}\left(\frac12+\frac1{2\pi}\right)$$
Solution by Sreeraj P, M.Sc Physics