I've been told that the radiation pressure of light can be understood(?) by considering a charged particle as a damped driven harmonic oscillator where the forcing term is the electromagnetic field, not neglecting the magnetic field term. In fact, I am told that the magnetic field term is responsible for the radiation pressure. I've already learned about the classical theory of light dispersion by treating the oscillator, neglecting that term. I'm trying to figure out the average force of light pressure on this electron-oscillator and having a difficult time. Since the equation for the force is $$\vec F=e(\vec E+\frac{1}{c}(\vec v\times \vec H)),$$ I'm imagining that there is no light pressure on the oscillating charged particle when it's at its extrema, and the max light pressure is when it's at the midpoint... but I can use information that I have externally to say that $$F=\frac{\Delta E}{c\Delta t}$$, where I already calculated the average rate of energy for the driven-damped oscillator differential equation neglecting the magnetic field, which oddly enough is given again for this problem. I simply don't understand how to connect what I know from the seemingly much simpler ways to derive and understand radiation pressure, to the magnetic field term.

Does anyone have any awareness or intuitive explanation for how radiation pressure comes out of the magnetic field force? I don't even understand how it is that it depends on a nonzero velocity (seems false).

• I have my doubts about this. A harmonic oscillator has a continuous, differentiable energy state; an bound electron has quantized energy states. And light pressure doesn't depend on promoting an electron into a higher orbital.
– g s
Nov 23 '21 at 16:50
• yes, I think this answers what you are talking about! physics.stackexchange.com/questions/497327/… Nov 23 '21 at 18:35

Ok, I have at least one better thought.

My confusion about why radiation pressure, if it comes out of the second term of the Lorentz force, seems to require a nonzero velocity of the thing it's acting on. This is fine in view of the fact that any charged particle will develop a $$\vec v$$ in the presence of the electric field. Then you end up with, say, a particle oscillating up/down with the electric field, and also in the presence of a right/left magnetic field, so (up)x(right)=forward: the radiation pressure, out of the magnetic field, pushes the particle forward. This picture makes clear how it is that we can say "the second term of the Lorentz force is responsible for the phenomenon of light pressure."

It does lead to a new question, which is, how does radiation pressure act on a neutral atom? can we just attribute it to a dipole concept, given the discreteness/distance between the electrons and nucleus? And/or, in the case of, say, a solar sail, do we just assume there is some number of charged particles?

I am still unsure how to get the relationship between the energy density and the force of the radiation pressure from the Lorentz force / oscillator equation, but it's ok. I can update with solutions later today.

• Could you explain the notation? It is not clear, whether this actually answers the question. Nov 23 '21 at 17:19