Question #43288

A uniform thin bar magnet of mass $m$, length $2L$, and magnetic dipole moment $\mu$ is pivoted at its center. The pivot is fixed to a vertical shaft that rotates with a constant angular velocity $\omega$. A uniform vertical magnetic field $B$ exists in the region. In the steady state, the magnet rests at a stable equilibrium angle $\theta_0 = \cos^{-1}(1/8)$ with the vertical axis.

The magnet is then removed, cut transversely into two equal halves, and one of the halves is pivoted at its own center on the same rotating shaft. Find the work done by an external agent to slowly rotate this half-magnet from its new stable equilibrium position to the horizontal plane ($\theta = 90^\circ$) in the rotating frame.