Question

A current carrying rectangular coil is placed in a uniform magnetic field. In which orientation will the coil not rotate?
A. The magnetic field is perpendicular to the plane of the coil.
B. The magnetic field is parallel to the plane of the coil.
C. The magnetic field is at ${45^ \circ }$ with the plane of the coil.
D. Always in any orientation.

Answer 1

Hint: To solve the above question, use the concept of torque experienced by a current carrying coil when it is placed in a uniform magnetic field. This torque is given by $\tau=NiAB \sin \theta=M~B~ \sin \theta$ , where A is the area of the loop and M is the magnetic dipole moment. The coil will not rotate when the value of the torque acting over it is 0. Use the formula to find out in which orientation will this torque be 0.

Formula used:
$\tau = NiAB\sin \theta $

Complete answer:
Torque on a current carrying loop placed in a uniform magnetic field is given by:
$\tau = NiAB\sin \theta $ … (1)
Where
$N$ is the number of loops in the coil,
$i$ is the current flowing through the coil,
$A$ is the area of the coil,
$B$ is the intensity of the magnetic field and
$\theta $ is the angle between the magnetic field and the axis of the coil.

This value of torque will be minimum when $\theta = 0$ or $\theta = \pi $ .

When $\theta = 0$ or $\theta = \pi $ , the value of torque on the current carrying rectangular coil will be 0 as $\sin \;0 = \sin \pi = 0$ .

As $\theta $ is the angle between the direction of the magnetic field and the axis of the coil, its value will be $0$ or $\pi $ , when the magnetic field is parallel or anti parallel to the direction of the axis.

Hence the plane of the coil should be perpendicular to the magnetic field. Thus, the correct option is A.

Note: For the coil to experience no torque (torque = 0), the cross product should give us a value equivalent to 0. This is only possible when the axis of the coil is parallel or anti parallel to the direction of the magnetic field.