JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Magnetic Effects of Current

The two straight portions of the wire lie along the line through the centre $O$, so for every element $d\vec{l}$ on them $d\vec{l}$ is parallel to $\vec{r}$ and the Biot-Savart contribution at $O$ vanishes. Only the semicircular arc produces a field at the centre, and for a semicircle $B=\frac{{\mu }_{0}I}{4R}$. Substituting, $B=\frac{4\pi \times 10^{-7}\times 14}{4\times 2.2\times 10^{-2}}$. The magnetic field at the centre $O$ is $2\times 10^{-4}\text{T}$.