Question

A bar magnet is suspended from the ceiling by a string as shown. If a uniform magnetic field directed parallel to the ceiling and to the left is then established, the resulting orientation of the magnet and the string in equilibrium will be correctly shown by: -

a)

b)

c)

d)

Answer 1

Hint: When a magnet is placed in a uniform magnetic field, draw the directions of force on the bar magnet which generates due to magnetic field. Net force is zero that means equal and opposite forces are acted on the magnet which align the bar magnet in a position which deviates magnet from the previous position.

Complete answer: When the magnetic field is pointed parallel to the ceiling and the left, the net force felt by a bar magnet fixed in a uniform magnetic field is zero. If we suspend the magnet by a string from its center so that it is easy to turn, it will change until its axis lies beside its pole, lying with the earth's magnetic north and south poles. The point which directs north is called the north pole and another pole is called the south pole.
When a bar magnet is placed in a uniform magnetic field, the two poles feel a force. The forces are identical in magnitude and reverse in direction, and do not have the same action line.
Net force = $mB (along +x direction) + mB (along -x direction)$
Torque = $MBsin\theta$
Two equal and opposite forces generate a torque that works to turn the magnet to adjust the bar magnet parallel to the field direction. Due to the coupled forces, the magnet will be as shown in the figure.

The string will remain vertical and the magnet will deviate.

Option (c) is correct.

Additional Information:
When angle is $90^{\circ}$ then torque will be maximum as $sin\theta=1$,
$Torque =MB$; torque gives rotational motion to magnet.
- when angle is $0^{\circ}$ then torque will be maximum as $sin\theta=0$ ,
$Torque =0$; magnet felt minimum torque.

Note:
Force on a pole is not equal to zero, note that force plays an important role. Net force is zero that means force equal in magnitude and opposite in direction acted upon the bar magnet. Due to the coupled forces, a torque comes into play which rotates the magnet and at equilibrium, both forces act and the bar magnet achieves a stable position in a uniform magnetic field.