A thin uniform bar magnet of mass 30 g and length 10 cm is suspended by a light thread at its centre in a uniform horizontal magnetic field of 0.2 T as shown. It is given a small angular displacement and performs simple harmonic motion with a time period of 2 s . The magnetic moment of the bar magnet is:

Step-by-step solution

The time period of oscillation of a bar magnet in a uniform magnetic field is given by: T = 2 I MB where I is the moment of inertia, M is the magnetic moment, and B is the magnetic field. The moment of inertia of a thin uniform bar magnet about an axis passing through its centre and perpendicular to its length is: I = mL^2 12 Given: m = 30 g = 30 10⁻³ kg L = 10 cm = 0.1 m I = 30 10⁻³ (0.1)^2 12 = 30 10⁻⁵ 12 = 2.5 10⁻⁵ kg m ^2 We are also given: T = 2 s B = 0.2 T Substituting these values into the time period formul