Electrodynamics-phase group velocity 1. The frequency-dependent dielectric constant in an insulator is approximately given by Ne 1 r (w) = 1+ MED j=1 w - w - yzw where N is the number density of molecules, Z is the number of bound electrons per molecule, e and m are the electron charge and mass, {w;} is the set of resonant frequencies which have widths { the electromagnetic wave. wi}, and wis the frequency of (f) The group velocity is defined as v = It is easier to evaluate the group velocity using the relation, since k = (w/c)(w) has all of the frequency dependence on the right hand side. Show that Up de 1 + 2 (g) Find the phase velocity and the group velocity in the low-frequency and high-frequency limits.