EXERCISE 7.17 At any given point r in a surface plasma wave, the electric field is given by (7.259), which we may write in the form E = Ege it (7.273) for some constant complex vector Eo. (a) Show that for real (negative) &(w), the complex electric field inside the conductor is E - Foe-" (n tipV-=(@)/so) (7.274) where Eo is a constant, and the choice of a positive sign for the second term is appropriate for a wave traveling in the p direction. (b) Show that if the electron motion is small compared with a wavelength (a necessary condition for the polarization to be a linear function of the field), the position of anelectron in the field of a surface plasma wave is -q Eo r = -i wt (n tip -8(w)/80) mo- (7.275) which corresponds to ellipses. Elliptical motions are characteristic of many types of surface waves, including water waves, where transverse motions and longitudi- nal motions are coupled by the presence of the surface. For a wave traveling in the p direction, do the electrons circulate in the clockwise or the counterclockwise direction?Ej =eel (kir-ot) (7.259)