Question

. 3. An electromagnetic plane wave of (angular) frequency w is traveling in the r direc- tion through the vacuum. It is polarized in the y direction, and the amplitude of the electric field is E (a) Write down the electric and magnetic fields, E(r, y, z, t) and B(x, y, z,t). Be sure to define any auxiliaru quantities you introduce, in terms of w, Eo, and the con stants of nature.] (b) This same wave is observed from "other" frame S, moving in the x direction with speed v relative to the original "home" frame system S. Find the electric and magnetic fields ins s', and express them in terms of the S coordinates: E(x, y,2,t,) and B(r,y'z',t). [Again, be sure to define any auxiliary quantities you introduce.] (c) What is the frequency w of the wave in S? What is the wavelength X in S? From! w, and X, determine the speed of waves in S. (d) What is the ratio of the intensity in S to the intensity in S? As a youth, Einstein wondered what an electromagnetic wave would look like if one could run along beside it at the speed of light. What can you tell him about the amplitude, frequency, and intensity of the wave, as v approaches c?

Answer 1

a) In frame S E^rightarrow = E_0 cos (kx minus wt) j^^B^rightarrow = E_0/c cos (kx minus wt) z^^C is velocity of light and k is wave vector b) Now frame 's' is having in x' direction with speed v co-ordinates of two frames are given as t = r (t' + v/c^2 x') Here r = 1/ squareroot 1 minus v^2/c^2 x = y (x' + v t') y = y' + z = z' The electric field transform as E'_x = E_x E'_y = r (E_y minus v B_z) E'_z = r (E_z + v B_y) E'_x = 0, E'_y = r (E_y minus v B_z) E'_z = 0 E'_y = r [E_0 cos (kx minus wt) minus v/c E_0 cos (kx minus wt) = r (1 minus v/c) E_0 cos [kr (x' + v t') minus wr (t' + v/c^2 x')]