One of the slides in Module 1 shows a snapshot of an electromagnetic wave in time, where the electric (E) and magnetic (H) fields appear to have the same phase at each point in space (i.e., the waves both peak at the same locations along the line of propagation), and E, H, and the direction of propagation are all perpendicular to one another. Given Maxwell's equations, is this necessarily true (assuming a monochromatic, plane EM wave in free space?) Examine this by assuming the wave is polarized in the x direction and propagates in the z direction, such that the electric field can be written as: E(F,t)= E cos(at-k.z)i a) Use Maxwell's equations to write an expression for the magnetic field H, and show whether it has the same phase as E at each point in z for a given time t. Hint: you may need to integrate H in time, and think about the constant of integration with regards to satisfying the wave equation and the stipulation that this is a "monochromatic wave. b) Using your results from part a, write an expression for the Poynting vector. Does it have the expected direction? Can its value ever drop below zero, and why do you think this is significant?