HW3-due Feb-15-2011

HW3-due Feb-15-2011 - NNSE 508 EM Home assignment # 3 Due:...

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Unformatted text preview: NNSE 508 EM Home assignment # 3 Due: February 15, 2011 1. For a normal incidence of plane monochromatic EM wave from a medium with impedance 1 to a medium with impedance 2, a) write the wave phasors (electric and magnetic fields) for incident, transmitted and reflected waves. Note: pay specific attention to relationships between signs that can be obtained from Maxwell equations. b) Applying boundary conditions show that reflection and transmission coefficients are as follows: r Er 2 1 Ei 2 1 t Et 22 1 r Ei 2 1 2. Electromagnetic radiation loses intensity when it reflects from surfaces with roughness greater than the wavelength . Assuming you would like to use the lowest energy source possible, determine the frequencies of EM waves which would be appropriate to characterize (a) cars on a road (b) the presence of mountains (c) micron-size voids in insulators (d) atomic steps on a single crystal and identify the types of EM waves present in each case (e.g. cosmic waves, UV, visible, etc.) 2K 2 1 coska , where a is the lattice 4. The dispersion relationship for lattice vibrations is M constant, M is the atomic mass, and K is an effective interatomic interaction (spring) constant. Sketch the dispersion relationship and derive an expression for the group velocity. 5. Show that at low frequencies (f < 1013 Hz) the reflectivity and conductivity of metals f 0 . Confirm that at these frequencies metals can be treated as “good conductors”. are related by Hugen-Rubens equation: R 1 4 6. Assuming that in alkali metals each atom provides one free electron, find in all alkali metals: a) electron density; b) electron mean free path at 300K; c) scattering time Given: Metal Li Na K Rb Cs Density, g/cm3 0.525 0.961 0.850 1.52 1.89 8.6 4.2 6.15 12.5 20 Specific resistivity -cm ...
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