329sp09hw9 - μ o in the region z> Calculate a The...

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ECE 329 Homework 9 Due: Thurs, Apr 2, 2009, 5PM 1. Region z> 0 is occupied by a perfect conductor. The region z< 0 is free space. a) Determine the unknowns b , β , c , d below such that Feld phasors ˜ E y 3 e - jβz + b e + jβz and ˜ H = c e - jβz + d e + jβz satisfy both the Maxwell’s equations in z< 0 region and the boundary condition equations at z =0 surface. Assume ω =2 π · 10 8 rad/s. b) Given the wave Felds of part (b), what is the surface current J s on z =0 plane. 2. A plane wave Feld E = 10 cos( ωt - βz x V m is propagating in vacuum in + z direction and is incident on z =0 plane which happens to be the boundary of a perfect dielectric having permittivity 4 ± o and permeability
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Unformatted text preview: μ o in the region z > . Calculate: a) The re±ected and transmitted electric Felds in terms of re±ection and transmission coe²cients R = η 2-η 1 η 2 + η 1 and T = 1 + R for the described interface. Express the Felds in phasor form. b) The incident, re±ected, and transmitted H Felds in A/m units. Express the Felds in phasor form. c) The time-average power per unit area transported by the incident, re±ected, and transmitted waves in W/m 2 units. Are the calculations compatible with energy conservation principle? Explain. 1...
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