A magnetic dipole executes angular motion in a uniform magnetic field. It is released from rest from an initial angular displacement θ₀ from the stable equilibrium position.
Which statement is correct?

Question

A magnetic dipole executes angular motion in a uniform magnetic field. It is released from rest from an initial angular displacement θ₀ from the stable equilibrium position.

Which statement is correct?

G1 Physics · Accepted Answer

The exact torque on a magnetic dipole is τ = -MB sinθ. Hence the exact equation of motion is I d²θ/dt² = -MB sinθ. For SHM, the restoring torque must be directly proportional to displacement θ. This occurs only for sufficiently small θ, when sinθ ≈ θ. Then, I d²θ/dt² ≈ -MBθ, which is the SHM equation. For finite amplitudes, sinθ is not equal to θ, so the motion is periodic but not exactly simple harmonic.