110324_hw7 - 3 A plane electromagnetic wave of frequency...

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March 24, 2011 PHYS 4132 Homework 7 Due date: March 31, 2011 1. Show that for a homogeneous, isotropic, initially charge free electrical conductor the charge density ρ is equal to zero for all times. 2. Consider an electromagnetic wave of angular frequency ω in a medium containing free electrons of density n e . a. Find the current density induced by E (negelect interactions between electrons). b. From Maxwell’ s equations write the differential equations for t he spatial dependence of a wave of frequency ω in such a medium. c. Find from these equations the necessary and sufficient condition that the electromagnetic waves propagate in this medium indefinitely.
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Unformatted text preview: 3. A plane electromagnetic wave of frequency and wave number k propagates in the +z direction. For z < 0, the medium is air with = and conductivity = 0. For z > 0, the medium is a lossy dielectric with > and > 0. Assume that = in both media. a. Find the dispersion relation (i.e., the relationship between and k) in the lossy medium. b. Find the limiting values of k for a very good conductor and a very poor conductor. c. Find the e-1 penetration depth for plane wave power in the lossy medium. 4. At what angle does a fish see the setting sun ? The index of refraction of water is 1.33....
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