A solid sphere of radius R carrying a uniform volume charge density ( ho) rotates around the z-axis at an angular velocity (omega). a) Find the magnetic field (vec{B}) at the center of the sphere. b) Find the magnetic dipole moment (vec{m}) of the sphere. c) Find the magnetic vector potential (vec{A}) outside the sphere. d) Now suppose we turn on an external magnetic field (vec{B}_{ext} = B_0 hat{x}), find the torque experienced by the rotating sphere.
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- The volume charge density is given as \( \rho \). - The volume of the sphere is \( V = \frac{4}{3} \pi R^3 \). - The total charge \( Q \) of the sphere is: \[ Q = \rho V = \rho \left( \frac{4}{3} \pi R^3 \right) \] Show more…
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