# Exam1 - ELEG 413 Field Theory II Exam#1 Spring 2011 Name...

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ELEG 413 Field Theory II Exam #1 Spring, 2011 Name ___________________________________________ Directions: Closed book and closed notes. You may NOT use a calculator. Four problems all worth 25pts each. Show your work clearly and write legibly for partial credit.

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1. The instantaneous electric field inside a conducting rectangular pipe (waveguide) is given by where z is the waveguide's phase constant. Assuming there are no sources within the free- space-filled pipe, determine (a) the corresponding instantaneous magnetic field components inside the conducting pipe (b) the phase constant z ) cos( ) sin( ˆ ) , , ( z t x a E a t z x E z o y
2. By solving the wave equation we find that the time harmonic electric field between two perfectly conducting plates (PEC) separated by a distance of, a, and filled with material with , and is given by where A, x and z are unknown constants. By applying boundary conditions and the dispersion relationship determine all of the unknown constants (where A, x and z ) x j x j z j y x x z Ae e e a z x E

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