Question #43259

A uniform solid sphere of mass $m \text{ (kg)}$ and radius $R \text{ (m)}$ has a total charge $q \text{ (C)}$ uniformly distributed throughout its volume. It is initially spinning with an angular velocity $\omega_0 \text{ (rad/s)}$ about an axis passing through its center. Uncharged cosmic dust falls radially towards the center of the sphere and sticks to its surface. This process continues slowly until the dust forms a uniform thin spherical shell of mass $m \text{ (kg)}$ and radius $R \text{ (m)}$ (assuming the thickness of the dust layer is negligible). No external torques act on the system during this process. If the initial magnetic dipole moment of the sphere is $\mu_0 \text{ (A}\cdot\text{m}^2\text{)}$, what is the final magnetic dipole moment $\mu_f$ of the system after the dust has settled?