2. Electromagnetic waves. An electromagnetic plane wave propagates along the positive x-axis. The electric and magnetic fields are given by E=Ecos(kxt) j, B = E c cos(kx t) k. (9) Here c = 1/00 is the speed of light in vacuum. Note that the electric and magnetic field amplitudes are related by the ratio c, as required by Maxwell's equations in a vacuum. The frequency and the wave-vector k are related via = kc. (a) Calculate u, the energy density of the field. Also calculate u, the time averaged energy density defined as u = 1 T T 0 dt u. Useful info: cos2(kx t) = 1 2 . (10) (11) (b) Calculate the Poynting vector S and the time averaged Poynting vector S. Recall that the Poynting vector corresponds to the energy per unit area delivered by the wave to a surface perpendicular to the direction of wave propagation, i. The magnitud