hw07 - Princeton University—Physics 501 Problem Set 7 Due...

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Unformatted text preview: Princeton University—Physics 501 Problem Set 7 Due: Dec. 6, 2011 1) (J7.4) A plane polarized electromagnetic wave of frequency ω in free space is incident normally on the flat surface of a nonpermeable medium of conductivity σ and dielectric constant . a) Calculate the amplitude and phase of the reflected wave relative to the incident wave for arbitrary σ and . b) Discuss the limiting cases of a very poor and very good conductor, and show that for a good conductor the reflection coefficient (ratio of reflected to incident intensity) is approximately R = 1- 2 ω c δ where δ is the skin depth. 2) The Earth’s ionosphere can be approximated by stratified horizontal planes (actually spherical shells) in which the electron density N increases with altitude z up to some maximum N max ’ 10 12 /m 3 , and then decreases. Snell’s Law applied to adjacent planes shows that a short-wave radio beam follows a path such that n ( z )sin θ ( z ) is constant, where n ( z ) is the refractive index as a function of height and θ is the angle of the beam with respect to the vertical. a) Neglecting the effect of the Earth’s magnetic field, show that a radio wave is reflected at or below the altitude at which the plasma frequency is equal to the...
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hw07 - Princeton University—Physics 501 Problem Set 7 Due...

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