COMEDK 2025 Morning Solved Paper

Concept:Each semicircular arc produces a magnetic field at the centre, and the two fields are perpendicular to each other because the arcs lie in different planes.Explanation:Both semicircular parts have the same radius $r = 2R$.For a circular arc carrying current $I$ subtending an angle $\theta$ at the centre, the magnetic field magnitude at the centre is $B = \frac{\mu_0 I \theta}{4\pi r}$.For a semicircle, $\theta = \pi$. So the field due to one semicircle is$B_{\text{each}} = \frac{\mu_0 I \pi}{4\pi (2R)} = \frac{\mu_0 I}{8R}$.One semicircle lies in the $xy$-plane, so its field is along the $z$-axis.The other lies in the $xz$-plane, so its field is along the $y$-axis.These two fields are perpendicular to each other.The net magnetic field magnitude is the vector sum of two equal perpendicular vectors:$B_{\text{net}} = \sqrt{B_{\text{each}}^2 + B_{\text{each}}^2} = \sqrt{2} \, B_{\text{each}} = \sqrt{2} \cdot \frac{\mu_0 I}{8R} = \frac{\mu_0 I}{4\sqrt{2}\,R}$.Answer:$\displaystyle \frac{\mu_0 I}{4\sqrt{2}\,R}$ (Option D).