Question

When a magnetic needle is placed in a nonuniform magnetic field it experiences 

1. a force but no torque a torque but no force force and torque neither a force nor a torque

2. A bar magnet held perpendicular to a uniform magnetic field as in the figure. If the torque acting on it is to be reduced to 1/4 by rotating the magnet towards the direction of the field, find the angle through which the magnet is to be rotated.

3. State whether the potential energy of the magnet increases or decreases after rotation. Justify your answer

Answer 1

1. force and torque 

2. When the bar magnet is perpendicular to the field Torque is maximum

τ = MBsinθ = MBsin(90) = MB

When rotated through an angle θ, torque is

\(\frac{\tau}{4}\) = MB sinθ

\(\frac{\tau}{\frac{\tau}{4}}=\frac{MB}{MBsin \theta}\)

4 = \(\frac{1}{sinθ}\)

θ = \(sin^{-1}\Big(\frac{1}{4}\Big)\) = 14.47°

Angle through which the magnet is to be rotated is 90 – θ = 75.53° 

3. Potential energy decreases. Potential energy is minimum when the magnet is parallel to the field.

U = MBcosθ. When rotated to 0° (to make magnet parallel to the field) Potential energy decreases.