110331_hw8

# 110331_hw8 - n 2/n 1 for which a circularly polarized wave...

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March 31, 2011 PHYS 4132 Homework 8 Due date: April 7, 2011 1. Two coaxial cylindrical conductors with radii r 1 and r 2 form a waveguide parallel to the z-axis. The region between the conductors is vacuum for z < 0 and is filled with a dielectric medium with dielectric constant ε 1 for z > 0 . a. Describe the TEM mode for z < 0 and z > 0 . b. If an electromagnetic wave in such a mode is incident from the left on the interface, calculate the transmitted and reflected waves. c. What fraction of the incident energy is transmitted ? What fraction is reflected ? 2. An electromagnetic wave which is coming from medium 1 is incident on a boundary layer between medium 1 and medium 2. The latter is optically thinner ( n 2 < n 1 ). a. What is the maximum value of the ratio
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Unformatted text preview: n 2 /n 1 for which a circularly polarized wave is produced in case of total reflection ? b. What is the incident angle for the wave on the boundary layer, such that for a given ratio n 2 /n 1 and after total reflection the wave is circularly polarized ? 3. A rectangular and hollow copper box has the following dimensions in x, y and z direction: a=2cm, b= 3cm, h=1cm. a. How many electromagnetic modes of wavelength λ are there in the range (4/√5) ≤ λ ≤ (8/√13) cm ? b. Find the wavelengths. c. Identify the modes by sketches of the E field. d. Approximately how many m odes are there in the range 0.01 ≤ λ ≤ 0.011 cm ? Recommended practice problem for independent self-study: • Griffiths problem 9.37 on p. 413...
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