Q 12-04-097JEE MainJEE Main 2024 (30 Jan, Shift 1)Medium
Two insulated circular loops $A$ and $B$, each of radius $a$ and carrying a current $I$ in the anticlockwise direction, are placed with a common centre $O$ in mutually perpendicular planes. The magnitude of the magnetic induction at the centre will be:
Answer: (C) $\dfrac{\mu_0 I}{\sqrt2\,a}$
Each loop gives $B_0 = \dfrac{\mu_0 I}{2a}$ at the centre, along its own axis. The two axes are perpendicular, so
$$B = \sqrt2\,B_0 = \frac{\sqrt2\,\mu_0 I}{2a} = \frac{\mu_0 I}{\sqrt2\,a}$$
Solution by Sreeraj P, M.Sc Physics