The characteristic impedance eta is given by while the

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Unformatted text preview: π π c= = = 108 ≈ 1.571 × 108 [m/s] . For comparison, the speed of k 0.2 2 light in vacuum is ≈ 3 × 108 [m/s] . 2.3.4 Part d FIND E (x, y, z, t) WORK E and H can be related through the characteristic impedance, η . The amplitudes follow the relationship, E = ηH , while the cross-product of E and H points in the direction of the wave vector, k . The characteristic impedance, eta, is given by η = μ , while the velocity is c = √1 , so η = μc. If the medium is non-magnetic, then μ ≈ μ0 = μ 4π × 10−7 [H/m], As such, E = xη sin(107 πt − 0.2z ) − yη sin(107 πt − 0.2z ) , where ˆ ˆ π8 10 2 = 2π 2 101 ≈ 197.4[Ω]. η = 4π × 10−7 × (2.5) (2.6) Again, for comparison, the characteristic impedance of vacuum is approximately 377Ω. 7 2.4 Problem 4 GIVEN 1-GHz uniform plane wave propagating in the z -direction in a medium with ˆ ˜ˆ permeability, μ, and permittivity, , characterized by...
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.013 at MIT.

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