Physics Question from JEE Main 2024 · 27 January, Shift 2

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1 = 2\pi \, \text{m}$ and $R_2 = 4\pi \, \text{m}$ carrying current $I = 4 \, \text{A}$ as per figure given below is $\alpha \times 10^{-7} \, \text{T}$. The value of $\alpha$ is: (Centre $O$ is common for all segments)

The figure shows: one closed loop of wire drawn about a common centre $O$, which is marked as a dot on a horizontal line. Above that line is a semicircle of the larger radius $R_2$, running from the point a distance $R_2$ to the left of $O$ over the top to the point a distance $R_2$ to the right of $O$; a dotted radius drawn from $O$ up to the right is labelled $R_2$. Below the line is a semicircle of the smaller radius $R_1$, running from the point a distance $R_1$ to the left of $O$ under the bottom to the point a distance $R_1$ to the right of $O$; a dotted radius drawn from $O$ straight down is labelled $R_1$. The two semicircles are joined by two straight segments that lie along the horizontal line through $O$ — one from $-R_2$ to $-R_1$ on the left and one from $+R_1$ to $+R_2$ on the right — so the whole wire is a single closed loop. No current-direction arrows are printed on the figure.