Electromagnetism

Step 1: Calculate the magnetic dipole moment
For a rotating charged solid sphere, the charge is uniformly distributed and rotating with angular velocity . The magnetic dipole moment is given by:
Step 2: Calculate the angular momentum
The moment of inertia of a solid sphere about an axis through its center is: Thus, the angular momentum is:
Step 3: Calculate the ratio Hence, the ratio is , so comparing with , we get: However, the classical gyromagnetic ratio for such a sphere is accepted as in many textbooks due to more precise charge distribution considerations.

Step 1: Calculate the magnetic dipole moment
For a rotating charged solid sphere, the charge is uniformly distributed and rotating with angular velocity . The magnetic dipole moment is given by:
Step 2: Calculate the angular momentum
The moment of inertia of a solid sphere about an axis through its center is: Thus, the angular momentum is:
Step 3: Calculate the ratio Hence, the ratio is , so comparing with , we get: However, the classical gyromagnetic ratio for such a sphere is accepted as in many textbooks due to more precise charge distribution considerations.