Explain, in a purely qualitative way, the mechanism by which a free and originally stationary electron gets pushed forward by the passage of a wave (radiation pressure!). In order to avoid a paradoxical backward push, show that we must have \(\mathbf{b}=\mathbf{a} \times \mathbf{e}\) tather than \(\mathbf{b}=-\mathbf{n} \times \mathbf{e}\). If the wave is circularly polarized, describe a possible motion of the electron. Deduce also that circularly polarized light carries angular momentum (in fact, of amount \(\sigma \omega\) per unit volume, if \(\omega\) is the rate of turning of the field).

Question: Explain the mechanism of radiation pressure on a free and originally stationary electron and how it relates to the angular momentum of circularly polarized light. Answer: When an electromagnetic wave passes through a free electron, the electron experiences a force due to the electric field of the wave, causing the electron to oscillate. This oscillating electron generates a magnetic field, which must be related to the electric field and wave vector to prevent backward push on the electron. In the case of circularly polarized light, the electron moves in a helical path due to the changing direction of the electric field, gaining both linear and angular momentum. The angular momentum per unit volume of circularly polarized light is given by \(\sigma \omega\), where \(\sigma\) represents the energy density of the wave, and \(\omega\) is the angular frequency of the wave.