Question

r of the electric field is given by ?= EOCRAA , vectors E and k lie in the x-plane. (a) Write down the expressions for all projections of electfic and magnetic fields as functions of variables x.y,z, and t and parameters En, o. ks, and k, if this wave is propagating in vacuum (b) Determine the spatial periods Ax and in the medium with permittivity e and permeability p if the angle betweenkand z-axis,0,1s given.? D.coSut

Answer 1

Given that Electric field E = E_0 e^1(kr wt) where, k = ku i + kz k then E_0 = E_0 x i + e_0 z k Then the magnetic field. B = 1/w (k times E) = 1/w Vertical-bar i kx E_0 z j 0 0 k kz E_0 z Vertical-bar = i (kr - wt) = 1/w [i(0) + j (kz E_0 x = kx E_0 z) + k [0]] e^i(kr - wt) = 1/w [kz - E_0 x - kx E_0 z) e^i[kr - wt] Therefore Ex - E_0 x e^i(k . r - wt) Ey = 0 Ez = E_0 z e^i k . r - wt) and B field Therefore Bx = 0, Bz = 0 By = 1/w [kz . E_0 x - k z E_0 z] e^i(k . r - wt) \r\n when k = squareroot kx^2 + kz^2: E_0 = squareroot E_0 x^2 + E_0 z^2 and k . r = k_x x + k_z z