Charge density in a rotating cylinder.
A solid metallic cylinder of radius \( R=0.5 m\) rotates about its axis with angular speed \(\omega=45 rad/s\). An external magnetic field of induction \(B= 10 mT\) is applied along the cylinder's axis. As a result, the cylinder becomes polarized. In other words, the charges in the bulk redistribute and the cylinder will have a constant volume charge density. Determine the magnitude of the charge density in Coulombs per cubic meter. Note, in this problem you may neglect the centrifugal force and the magnetic field created by the rotating electrons.