6. Consider a region of vacuum (i.e., having no charges, currents, or any matter in it). This region has an electromagnetic plane wave propagating along the +2 direction with frequency a) and its electric eld E pointing along the x axis. This region also has a second electromagnetic plane wave With the same with frequency a) that propagates along the z direction With its electric eld E pointing along the x axis (i.e., the total elds are the sum of these two plane waves). Both plane waves have the same electric eld amplitude E0. a) Show that the total electric eld E can be written as f (z)g(t)i and the total magnetic eld B can be written as h(z) j (1'))? , where j; g, and h are each a function of a single variable. Find z), g(t), 11(2), and j(t). b) Find u(z,t), the energy density as a function of position along the z axis and time (it will be independent of x and y). c) Make a sketch of u(z) for three cases: cot = 0, cut = 7r/4, and out = 7r/2. d) Find the Poynting vector S(z,t) (it will be independent of x and y). Make a sketch of (or describe in words) how energy ows along the z direction. Is there a net flow (i.e., averaged over space and time) of energy in this system