This problem inspired by the 2008 Guangdong Province Physics Olympiad
Two infinitely long concentric hollow cylinders have radii a and 4 a. Both cylinders are insulators; the inner cylinder has a uniformly distributed charge per length of +\lambda; the outer cylinder has a uniformly distributed charge per length of -\lambda.
An infinitely long dielectric cylinder with permittivity \epsilon=\kappa \epsilon_{0}, where \kappa is the dielectric constant, has a inner radius 2 a and outer radius 3 a is also concentric with the insulating cylinders. The dielectric cylinder is rotating about its axis with an angular velocity \omega \ll c / a, where c is the speed of light. Assume that the permeability of the dielectric cylinder and the space between the cylinders is that of free space, \mu_{0}.
a. Determine the electric field for all regions.
b. Determine the magnetic field for all regions.