A sphere of radius R carries a surface-charge distribution σ in the region of θ ∈ [π/2−α, π/2 +α], α is a fixed parameter. The rest of the sphere has no charge. The sphere is rotated about the z axis with constant angular velocity ω. (a) (20 pts) Find the magnetic dipole moment ~m. (b) (10 pts) Demonstrate that your solution is correct by considering two limits: α → π/2, α → 0. In the second limit assume that the total current is held fixed.