hw9 - mode TM mn 1 Phys 3327 Fall 2010 HW 9 Due Wednesday...

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Phys 3327 Fall 2010 HW 9 Due Wednesday 11/10/10 in lecture Homework 9 Wave Guides (2) Ex. 9.1: Dielectrics in Capacitors (Conceptual) Make careful sketches of the D and E ±elds for a charged capacitor with a wedge of dielectric with permittivity ± inserted, see diagram below. Make sure you explain your diagrams, either with other supplementary diagrams and/or a short written explanation. Ignore edge effects. - + (a) Ex. 9.2: TM Modes in a rectangular waveguide Consider a rectangular waveguide with walls made of an ideal conductor. The rectangular cross section has sides of length a and b<a . The goal of this problem is to ±nd the transverse magnetic (TM) modes of this waveguide, identify the cut-off frequency for each mode, and the amount of energy transmitted. In this exercise, we choose coordinate axes as shown in the ±gure below. a) What are the boundary conditions that E z ( x, y ) has to satisfy? b) The z dependence of the ±elds is described using the phase factor e i ( kz - ωt ) . What is the dispersion relation k ( ω ) for this waveguide? What is the cut-off frequency for the
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Unformatted text preview: mode TM mn ? 1 Phys 3327 Fall 2010 HW 9 Due Wednesday 11/10/10 in lecture c) Find the transverse components of the electric and magnetic ±elds in the waveguide. d) What is the magnitude and direction of the Poynting vector for the mode TM mn , averaged over time and over the cross section of the wave guide? Ex. 9.3: Waveguide with circular cross section Heald & Marion ex. 7-13. Suggested problems for further study: • Loss A rectangular hollow-conductor waveguide of dimensions a × b has walls made of good, but not perfectly conducting metal. Estimate the loss per unit length for the funda-mental ( n = 1) mode in this waveguide. Your answer should contain the dependence on the skin depth δ of the wall conductor, the frequency ω of the EM wave, a and b (if applicable), but you need not specify the precise numerical prefactor. • Resonant Cavity : Heald & marion, ex. 7-14. 2...
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hw9 - mode TM mn 1 Phys 3327 Fall 2010 HW 9 Due Wednesday...

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