Question

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)?

Answer 1

(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,