Consider a particle of charge q and mass m, free to move in the xy plane in response to an electromagnetic wave propagating in the z direction (Eq. 9.48—might as well set δ=0).
(a) Ignoring the magnetic force, find the velocity of the particle, as a function of time. (Assume the average velocity is zero.)
(b) Now calculate the resulting magnetic force on the particle.
(c) Show that the (time) average magnetic force is zero.
The problem with this naive model for the pressure of light is that the velocity is 90∘ out of phase with the fields. For energy to be absorbed, there's got to be some resistance to the motion of the charges. Suppose we include a force of the form −γmv, for some damping constant γ.
(d) Repeat part (a) (ignore the exponentially damped transient). Repeat part (b), and find the average magnetic force on the particle.