EAD234B_Homework4_2010

EAD234B_Homework4_2010 - EAD 234B E&M Homework#4 Due...

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EAD 234B: E&M Homework #4 Due Thursday, April 29, 2010 (1) A rectangular waveguide with a constant cross section and perfectly conducting walls contains a curved section as sketched below. Also indicated is a local Cartesian coordinates system where the z-axis and y-axis remain tangent and normal to the walls, respectively. (a) The scalar function Φ satisfies ( ) 22 2 /, 0 cy z ω ⎡⎤ = ⎣⎦ , where 2 // x y ∇ =∂ +∂ ∂ . Show that the four vacuum Maxwell equations and conducting wall boundary conditions are satisfied by time harmonic transverse electric (TE) modes of the form (b) Suppose that the curvature κ (z) of the sidewall at any point on the guide satisfies κ a 1 so the Laplacian operator in the local coordinate Cartesian coordinate system is well approximated by Separate variables in the Helmholtz equation and show that propagating modes exist in the straight portion of the guide (at least) when ω > π c/a.
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This note was uploaded on 05/14/2010 for the course EAD 234 taught by Professor Ncl during the Spring '10 term at École Normale Supérieure.

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EAD234B_Homework4_2010 - EAD 234B E&M Homework#4 Due...

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