329sp08hw4 - ECE 329 Homework 4 Due 5PM 1 Consider a...

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ECE 329 Homework 4 Due: Feb 11, 2008, 5PM 1. Consider a time-varying electric feld specifed as E yE o cos( ωt - βz ) V/m where E o (amplitude), ω (radian Frequency), and β (wavenumber) are constant real scalars. a) ±ind the corresponding magnetic felds B and H = μ - 1 o B using ±araday’s law ∇× E = - B ∂t (in di²erential Form) and an additional constraint that B =0 iF E o =0 . b) Show that E specifed above satisfes Gauss’s law ∇· D = ρ with D = ± o E and ρ =0 . c) Show that D and H From above satisFy the Ampere’s law ∇× H = J + D ∂t with J =0 and ω 2 β 2 = 1 μ o ± o c 2 . d) What is the numerical value oF c (speed oF light) in SI? e) Suppose that β =+ ω c , in consistency with the constraint in (c), and ω =2 π × 10 6 rad/s. Plot (by hand, not with computer) E y = E o cos( ωt - βz ) in that case as Function oF z at time instants t =0 and t = π/ 4 ω , and From the displacement oF one oF the crests oF E y waveForm inFer the velocity of propagation , v p , oF the feld E yE y in z direction.
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This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

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329sp08hw4 - ECE 329 Homework 4 Due 5PM 1 Consider a...

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