Rotating Dielectric Cylinder Between Charged Cylinders · USAPhO 2012 #A3
Physics · electromagnetism
Problem
This problem inspired by the 2008 Guangdong Province Physics Olympiad
Two infinitely long concentric hollow cylinders have radii a and 4a. Both cylinders are insulators; the inner cylinder has a uniformly distributed charge per length of +λ; the outer cylinder has a uniformly distributed charge per length of −λ.
An infinitely long dielectric cylinder with permittivity ε = κε₀, where κ is the dielectric constant, has a inner radius 2a and outer radius 3a is also concentric with the insulating cylinders. The dielectric cylinder is rotating about its axis with an angular velocity ω ≪ 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, μ₀.
a. Determine the electric field for all regions.
b. Determine the magnetic field for all regions.