Derive the in homogeneous wave equation satisfied by the electric field E(r, t) in a system where ρ(r, t) = 0 but j(r, t) ≠ = 0. Show that this equation has a plane wave solution E = E0 exp[i(k · r − ωt)] for a system of non-interacting electrons (number density n) that respond to an electric field E according to Newton’s law. Display the dispersion relation ω(k) explicitly.