Q. A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotation it from this position. The angle of rotation is
A) $60{^\circ}$
B) $45{^\circ}$
C) $30{^\circ}$
D) $75{^\circ}$
Explanation
(a) Torque, $\tau = MB\sin\theta$
Where $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta = 90{^\circ}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \tau = MB$
Given, $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \tau_{2} = \frac{1}{2\ }\tau_{1}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ MB\ \sin{\theta = \frac{1}{2}\ MB}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {sin\ \theta}{= \frac{1}{2}\ }$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta = 30{^\circ}$
Angle of rotation is $= 90{^\circ} - 30{^\circ} = 60{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.