The following considers electromagnetic wave propagating in free-space (without charges or currents). (a) State the Maxwell's equations in terms of E and H for the free-space. (b) Should that the four equations are satisfied by: C E = Eo cos (w²t)) x s(w (²-t)) y Eo H COS CHO for some constants Eo and @o, where c is the speed of light in free-space.

A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eo and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N) has electric field given by E₁ = Eoiû Re [exp j(k-r - wt+d;)]. From this, prove that the total intensity Inet including interference is given by Ec|² 27⁰ where the complex amplitude E, is defined by Inet and 70 is the impedance of free space. N Ec = Eoi exp(joi), 7 i=1