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Project Help - ECE3025 Summer 2011 Class Project Help Paul...

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ECE3025, Summer 2011, Class Project Help Paul Voss 1 Advice Advice for Project 2: The nice thing about this project is that it is two dimensional, not three dimensional. This means that we will either have perpendicular or parallel polarization and the equations will simplify quite a bit. In order to derive the following answer, you need to take the following steps: 1. We want to have the fields not vary as z changes, but have them do vary as x and y changes. If we write out Maxwell’s Equations in Cartesian coordinates, but set all z derivatives equal to 0, we get ∂H x ∂t = 1 μ - ∂E z ∂y (1) ∂H y ∂t = 1 μ ∂E z ∂x (2) ∂H z ∂t = 1 μ ∂E x ∂y - ∂E y ∂x (3) ∂E x ∂t = 1 ∂H z ∂y - σE x (4) ∂E y ∂t = 1 - ∂H z ∂x - σE y (5) ∂E z ∂t = 1 ∂H y ∂x - ∂H x ∂y - σE z (6) 2. Please notice that we have included loss ( σ ) here, but in our simulations, σ = 0, so we have only dielectrics in our region of interest. We may as well set σ = 0 from now on. Please notice also that Equations 1, 2, and 6 are totally independent of Equations 3, 4, and 5.
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