TM-polarized plane wave is incident on a PEC cylinder of radius a aligned along the z-axis in free space. The cylinder is coated with a material layer of radius b with complex permittivity ? c(ω) and permeability µ(ω) ˜ . Apply the boundary conditions on the surface of the cylinder and across the interface between the material and free space and determine the total field both internal and external to the material layer.