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chap10 013 - 10.30 CHAPTER 10 WAVES IN ISOTROPIC MATERIALS...

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Unformatted text preview: 10.30 CHAPTER 10. WAVES IN ISOTROPIC MATERIALS rubber ' 3.5 silicon fresh water sea water copper Problem 10.21: The properties of sev- eral materials are listed to the right. For what frequencies can they be considered good conductors and for what frequencies are they good dielectrics? (Assume that >> means a factor of ten.) Problem 10.22: Show that the real and imaginary parts of the complex wavenumber k = k’ — jk” in terms of the complex permittivity 2-: = 5' — je” (With p = no) are given b y 1/2 1 1 a 21/2 r saw->1 El 1 1 e” 2 1/2 H: ,0 __ _ 1 __ k w “05 2+2 +(e’) a. Which are the physically sensible solutions of the quadratic equations for (k’)2? b. Using the binorniai expansion (1 + :5)11 m 1 + nr + %n(n — Us2 + ..., for small 1: and any n, show that the “low loss” approximations for k’ and k” are given by 1 E” 2 I 5” k, W WVMDE’ l + g (E) and k” m in) M05' (3) Problem 10.23: A wave is described by 1/2 E = E06: — j2y)ef(”‘—'“) in a lossy dielectric with 5/50 = 4 — 3'2 x 10—3. If the wave frequency is 1 GHz and the average power flux < S > at z = 0 is 10 W/m2, find a. k', k”, A, and E0. b. the wave attenuation (in dB) in 200 m. c. the Poynting vector at z = 200 m. d. the amplitude of E3: at z = 200 m. Problem 10.24: A circularly polarized wave with f = 300 MHz propagates in a slightly lossy dielectric. The measured wavelength is 40 cm and the wave attenuates 10 dB in 100 In. What is the complex dielectric constant? Assume [1 = #0- Problem 10.25: A plane wave propagates in a slightly lossy dielectric. The wave— length of the wave is measured and found to be 15 cm. At 2 = 0, the power flux is 100 watts/m2 and at z = 10 In it has decreased to 30 watts/m2. The phase velocity of the wave is 1.5 x 108 m/s. a. What is the wave frequency? ...
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