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Assignment5

# Assignment5 - in phasor form(b Determine the real...

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EC 501 Assignment 5 (2008) (Uniform plane waves and plane waves at boundaries) 1. An H field in free space is given as H (x, t) = 10 cos(10 8 t - β x) â y A/m. Find: (a) β ; (b) λ ; (c) E (x, t) at P (0.1, 0.2, 0.3) at t = 1 ns. 2. A uniform plane wave in free space has electric field vector given by E s = 10 e jβx â z + 10 e jβx â y V/m. (a) Describe the wave polarization: (b) Find H s ; (c) determine the average power density in the wave in W/m 2 . 3. The plane y=0 defines the boundary between two different dielectrics. For y < 0, ε′ R1 = 1, μ 1 = μ 0 , and ε″ R1 = 0; and for y > 0 , ε′ R2 = 5, μ 2 = μ 0 , and ε″ R2 = 0. Let E z1 + = 150 cos(ω t – 8y) V/m, and find: (a) ω ; (b) H 1 + ;(c); H 1 - . 4. A left-circularly polarized plane wave is normally incident on to the surface of a perfect conductor. (a) Construct the superposition of the incident and reflected waves
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Unformatted text preview: in phasor form. (b) Determine the real instantaneous form of the result of part a. (c) Describe the wave that is formed. 5. A dielectric waveguide is shown in the figure below with refractive indices as labeled. Incident light enters the guide at angle φ from the front surface normal as shown. Once inside, the light totally reflects at the upper n 1- n 2 interface, where n 1 > n 2 . All subsequent reflections from the upper and lower boundaries will be total as well, and so the light is confined to the guide. Express , in terms of n 1 and n 2 , the maximum value of φ such that total confinement will occur, with n = 1. The quantity sin φ is known as the numerical aperture of the guide....
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