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ECE309-2008-hw10

ECE309-2008-hw10 - ECE 309 — Electromagnetic Fields...

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Unformatted text preview: ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 10 — Electromagnetic Waves Due: Friday, December 5 1. The electrical constitutive parameters of moist earth at a frequency of 100kHz are: σ = . 01 S/m, r = 30 , and μ r = 1 . Assuming that the electric field of a uniform plane wave at the earth-air interface (just inside the earth) is ~ E , find: (a) The distance through which the wave must travel before it is attenuated by 3dB. (b) The wavelength inside the earth (in meters). (c) The phase velocity inside the earth (in m/sec). (d) The intrinsic wave impedance in the earth. 2. Derive the following general expressions for the attenuation and phase constants for conduct- ing media: α = ω r μ 2 n r 1 + σ ω 2- 1 o 1 / 2 β = ω r μ 2 n r 1 + σ ω 2 + 1 o 1 / 2 3. Consider the situation of normal incidence at a lossless dielectric slab of thickness d in air, as shown below: (a) Find E r , E + 2 , E- 2 , and E t in terms of E i , d , 2 , and μ 2 ....
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ECE309-2008-hw10 - ECE 309 — Electromagnetic Fields...

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