Due: Friday, 14 May 2004
22. (a) For a dilute plasma, find expressions for the phase and group velocity. Which is larger? Are there problems? (b) A strong radio source located a distance d from the Earth, emits periodic pulses every 16 milliseconds. The pulses are not monochromatic. Our detector is sensitive to radiation centered on 408 MHz over a band of width 2 MHz. The space between the Earth and the pulsar has electron number density ne. Find an expression for the smearing of the pulse. That is, find an expression for the difference in arrival times for waves with different frequencies. Assume that the plasma frequency is << 408 MHz.
23. Transverse electromagnetic waves propagate along the z-axis through an electron gas of ne electrons per unit volume. A uniform B field is aligned parallel to the propagation direction. Neglecting damping, write down the equation of motion for the free electrons driven by circularly polarized light. Show that only circularly polarized waves propagate without change and find the index of refraction.
24. Problem 9.27
25. Problem 9.28
26. If a plane electromagnetic wave is incident on a free particle of charge e and mass m, it will cause the charge to oscillate and hence, to radiate. The overall process can be thought of as scattering of radiation with a cross-section defined by the ratio of the radiated power to the incident power. Find the cross-section for the above situation and evaluate it numerically when the free particle is an electron. Answer: 0.66x10-24 cm2, the Thomson cross-section.