Q 12-04-213JEE MainJEE Main 2019 (9 Apr, Shift 1)Medium
A rectangular coil (dimension $5\ \text{cm}\times2.5\ \text{cm}$) with 100 turns, carrying a current of $3\ \text{A}$ in the clockwise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of $1\ \text{T}$ is applied along X-axis. If the coil is tilted through $45^\circ$ about Z-axis, then the torque on the coil is
Answer: (D) $0.27\ \text{N m}$
In the X-Z plane the coil's magnetic moment is along Y, perpendicular to $\vec B$. After tilting $45^\circ$ about Z, the moment makes $45^\circ$ with X (the field).
$$\tau = NIAB\sin45^\circ = 100\times3\times(5\times2.5\times10^{-4})\times1\times0.707 \approx 0.27\ \text{N m}$$
Solution by Sreeraj P, M.Sc Physics