homework4

# Engineering Electromagnetics with CD (McGraw-Hill Series in Electrical Engineering)

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 4 Due Tuesday, April 26 th in class 1. Region 1, z < 0, and region 2, z > 0, are described by the following parameters: ε 1 = 100 pF/m, μ 1 = 25 μH/m, ε ’’ 1 = 0, ε 2 = 200 pF/m, μ 2 = 50 μH/m, and ε ’’ 2 / ε 2 = 0.5. If E 1 + = 600 e - α 1 z cos(5 × 10 10 t – β 1 z) a x V/m, find: (a) α 1 (b) β 1 (c) E s1 + (d) E s1 - (e) E s2 + 2. In a dispersive material the refractive index n depends on the frequency. Electromagnetic pulses propagating in such materials will experience broadening. Consider a plane wave of frequency ω 0 that is temporally modulated by a Gaussian pulse 2 ) ( 2 1 0 ) , 0 ( T t e E t z E = = . a). Show that
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• Spring '05
• Psaltis
• Electromagnet, Wavelength, Fundamental physics concepts, Electromagnetic Engineering, amplitude transmittance, pulse envelope propagates

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