The position vector x for an electron moving with velocity much less than c in a plane monochromatic wave epsilon e_0 cos(omega t - kz) is determined by the equation of motion md^2 x/dt^2 = e epsilon e_0 cis (omega t - kz). show that the refractive index of an electron gas is given by eq. (3.14.13). assume that in the ionosphere the refractive index for 100-mhz radio waves is 0.90 and that the free electrons make the greatest contribution to the index. estimate the number density of electrons. why is the contribution of positively charged ions to the refractive index much smaller? choose an am and an fm radio station in your area and compare their frequencies to the plasma frequency of the ionosphere.