JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Magnetic Effects of Current

The hairpin consists of two straight semi-infinite wires and a semicircular arc.

For each straight wire at distance $r$ from point P: $B_{\text{straight}}=\frac{{\mu }_{0}I}{4\pi r}$

For the semicircular arc of radius $r$: $B_{\text{arc}}=\frac{{\mu }_{0}I}{4r}$ (half of a full circular loop)

All three contributions point in the same direction (into or out of the page). Total field:

$B=2\times \frac{{\mu }_{0}I}{4\pi r}+\frac{{\mu }_{0}I}{4r}=\frac{{\mu }_{0}I}{4\pi r}(2+\pi )$