(a) Let E = E 0 cos(kz t)x + E 0 cos(kz + t)x. Write E(z, t) in simpler form and find the associated

(a) Let E = E₀ cos(kz − ωt)x̂ + E₀ cos(kz + ωt)x̂. Write E(z, t) in simpler form and find the associated magnetic field B(z, t).
(b) For the fields in part (a), find the instantaneous and time-averaged electric and magnetic field energy densities. Find also the instantaneous and time-averaged energy current density.

(c) Let E = E₀ cos(kz − ωt)x̂ + E₀ sin(kz + ωt)ŷ. Determine the polarization of this field at z = 0, z = λ/8, z = λ/4, z = 3λ/8, and z = λ/2.
(d) Show that the field in part (c) can be written as a superposition of an LHC standing wave and an RHC standing wave.
(e) Find the time-averaged Poynting vector as a function of z for the field in part (c).