Let A(, z, t) = U(, z, t) z be a Lorenz gauge vector potential where U(,

Let A(ρ, z, t) = U(ρ, z, t) ẑ be a Lorenz gauge vector potential where U(ρ, z, t) = u(ρ, z) exp(−iωt) is an azimuthally symmetric, beam-like solution of the scalar wave equation which propagates in the z-direction. Show that the magnetic field B(ρ, z, t) and electric field E(ρ, z, t) are both linearly polarized, but that the latter is not transverse.