# Radiation pressure - classical description

1. May 22, 2010

### dan_b_

As I understand it, when an e-m wave with low frequency strikes a material with a much higher resonance frequency, the displacement of the electron relative to the atom will be in phase with the electric field (well opposite phase if you account for the negative charge).
When the electric field incident on an atom is at the maximum value of the wave cycle
(ie. E(t) = Eo=Emax) , the velocity of the vibrating electron would be zero (at a turning point). The magnetic field, though also a maximum at this time (t), would produce no force on the electron at this moment.

If one explores the force produced by the magnetic field on the electron a small time before time t (e.g. 10% of a cycle earlier, when the vibrating electron is in motion) one finds that the electron (say moving in the +y direction) will experience a lateral force, say in the direction of the incident radiation. But if one compares this to the force experienced a short moment after time t (e.g. 10% of a cycle later) the electron is moving in the opposite direction (having passed the turning point). The B field still has the same sign at this moment, but the electron's velocity has reversed - the lateral force produced by the B-field must also be reversed. As I see it, radiation pressure is not predicted - the lateral force on the matter would be oscillatory. The lateral force produced would average to zero over a cycle.

I have read Poyting vector analyses that generate the radiation pressure, but they never seem to discuss the instantaneous relationships of the phases of interest.

Is there something wrong with my thinking? Is there an article that accounts for the phase
relations in the radiation pressure analysis? I would be most grateful if I could get the help to "get over this one"!

2. May 22, 2010

### Creator

That's because it is usually the time averaged Poynting vector that is used to find radiation pressure.

Yes there is, but I'm too lazy to LaTex it; It is given here (middle of the page under the heading "DERIVATION"):

http://en.wikipedia.org/wiki/Poynting_vector

Creator

3. May 23, 2010

### dan_b_

I had a look at the Poynting vector information that you recommended - thank you for the suggestion. It seems like Poynting vector arguments justifiably ignore the nature of the interaction of the wave and matter, in that conservation of E and p are sufficient to predict a formula for the amount of radiation pressure that an e-m wave can exert on matter. This would justify the time averaging approach. But I am still interested in understanding the classical mechanism of the interaction (the meat rather than the potatoes, if you will).