# 329sp09hw9sol - ECE-329 Spring 2009 Homework 9 — Solution...

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Unformatted text preview: ECE-329 Spring 2009 Homework 9 — Solution April 4, 2009 1. Region z > is occupied by a perfect conductor and region z < is free space. We will apply Maxwell’s boundary conditions to fully determine the field phasors in region z < considering that they have the following form ˜ E = 3ˆ ye- jβz + b e jβz and ˜ H = c e- jβz + d e jβz . a) The phasors above correspond to the superposition of two plane waves propagating into + z and- z directions. Given that the wave frequency is ω = 2 π × 10 8 rad / s , and the propagation velocity in free space is c = 3 × 10 8 m / s , the propagation constant β is β = ω c = 2 π 3 rad m . Since the tangential component of ˜ E must be continuous across the interface and noting that the electric field in the conductor is zero, we can write ˆ n × ˜ E z =0 = where ˆ n = ˆ z . Replacing terms, we get that ˆ z × (3ˆ y + b ) = and thus b =- 3ˆ y....
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329sp09hw9sol - ECE-329 Spring 2009 Homework 9 — Solution...

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