JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Magnetic Effects of Current

Only the circular arcs contribute at the centre $O$; the straight radial segments lie along the lines to $O$ and produce no field there. An arc of radius $r$ subtending angle $\varphi$ gives $B=\frac{{\mu }_{0}I\varphi }{4\pi r}$. With the two arcs of radii $3$ cm and $5$ cm each subtending $\frac{\pi }{4}$ and their fields both pointing into the page, $B=\frac{{\mu }_{0}I}{4\pi }\cdot \frac{\pi }{4}\left(\frac{1}{0.03}-\frac{1}{0.05}\right)$. Putting in $I=10$ A brings this close to $1.0\times 10^{-5}$ T.