A bar magnet of magnetic moment 1.5 J T −1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?
(b) What is the torque on the magnet in cases (i) and (ii)?
(a)Magnetic moment, M = 1.5 J T−1
Magnetic field strength, B = 0.22 T
(i)Initial angle between the axis and the magnetic field, θ1 = 0°
Final angle between the axis and the magnetic field, θ2 = 90°
The work required to make the magnetic moment normal to the direction of magnetic field is given as:
(ii) Initial angle between the axis and the magnetic field, θ1 = 0°
Final angle between the axis and the magnetic field, θ2 = 180°
The work required to make the magnetic moment opposite to the direction of magnetic field is given as:
(b)For
case (i):
∴Torque,
For
case (ii):
∴Torque,
