Question

Given figure shows the north and south poles of a permanent magnet in which an ' $n$ ' turn coil of crosssectional area ' $A$ ' is resting, such that, when a current ' $I$ ' is passed through the coil, the plane of the coil makes an angle ' $\theta$ ' with respect to direction of magnetic field ' $B$ '. If the plane of magnetic field and the coil are horizontal and vertical respectively, the torque on the coil will be

• A. $n I A B \cos \theta$
• B. $n I A B \sin \theta$
• C. $n I A B$
• D. None of the above since the magnetic field is radial

Answer 1

Answer: (C)

According to question, torque acting on the coil in magnetic field $B$ is given as
$\tau=n I A B \sin \theta$
When the plane of magnetic field and the coil are horizontal and vertical respectively, then normal of coil makes $90^{\circ}$ with the direction of magnetic field.
$\therefore \theta=90^{\circ}$
$\therefore \tau=n I A B \sin 90^{\circ}=n I A B$