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Question:

Show that the time period (T) of oscillations of a freely suspended magnetic dipole of magnetic moment (m) in a uniform magnetic field (B) is given by T = 2π√(I/mB), where I is the moment of inertia of the magnetic dipole.

Solution:

τ=M→×B→=MBsinθ
For small angle θ
τ=MBθ
α=(MBI)θ
Comparing with angular SHM
ω²=MBI
T=2πω=2π√(I/mB)
where, m=magnetic moment
I=moment of inertia
B=magnetic field intensity