(Solution) - A magnetic field is applied to a freely floating uniform -(2025 Original AI-Free Solution)

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A magnetic field is applied to a freely floating uniform iron sphere with radius R = 2.00mm. The sphere initially had no net magnetic moment, but the field aligns 12% of the magnetic moments of the atoms (that is, 12% of the magnetic moments of the loosely bound electrons in the sphere, with one such electron per atom). The magnetic moment of those aligned electrons is the sphere's intrinsic magnetic moment
. What is the sphere's resulting angular speed ??