Question #43028

A cylindrical sample of a high-resistivity ferrimagnetic material of volume $V = 5.0 \times 10^{-4} \text{ m}^3$ is suspended vertically by a light torsional wire of torsional constant $C = \frac{2.0}{\pi^2} \text{ N}\cdot\text{m/rad}$. A uniform horizontal magnetic field $\vec{B}$ is applied. Initially, the wire is untwisted, and the sample is in equilibrium. An external agent slowly rotates the cylinder around the vertical axis by exactly one full turn ($2\pi \text{ rad}$) and holds it in this new position. During this $360^\circ$ rotation, the magnetization of the sample undergoes exactly one complete hysteresis cycle. Assume the energy dissipated per unit volume during this rotation is equal to the area of the material's $B-H$ hysteresis loop, which is given as $A_H = 4000 \text{ J/m}^3$. Assuming eddy current losses are negligible, what is the total work done by the external agent?