1School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2007 Homework 5 Due on Sep. 28, 2007 by 5:00 PM Reading Assignments: i) Review the lecture notes. ii) Review sections 1.1-1.6 of the paperback book Electromagnetic Waves. We have officially started the paperback textbook and will follow it till the end of the semester. Problem 5.1: (Vector Calculus and Plane Waves) Consider a plane wave whose E-field vector phasor is given by the following expression: Where kr and the unit vector nˆ can be decomposed into components as follows: Prove the following three relations: a) ()()rkjoeEnkjrErrrrr.ˆ−×−=×∇ b) ()()rkjoeEnkrErrrr.22ˆ−−=∇ c) ()()rkjoeEnkjrErrrrr.ˆ..−−=∇ Problem 5.2: (Polarization of Plane Waves) a) Find the Polarization (i.e., linear, circular, or elliptical, and left-handed or right-handed) of the following plane waves: i) ()()xjkoeEzyjrE−+=ˆˆrr ii) ()()( )[]yjkoeEjzjxrE 13ˆ2ˆ+++=rr iii) ()[]zjkoeHyjxrHˆˆ−=rr iv) ()()()2ˆˆyxjkoeEyxrE+−+−=rr ()rkjoeEnrErrrr.ˆ−=znynxnnzkykxkkzyxzyxˆˆˆˆˆˆˆ++=++=r2 b) Find the magnetic field (or the electric field - whichever is not given) for the following plane waves: i) ()()xjkoeEzyjrE−+=ˆˆrr ii) ()()( )[]yjkoeEjzjxrE 13ˆ2ˆ+++=rr iii) ()[]zjkoeHyjxrHˆˆ−=rr iv) ()()()2ˆˆyxjkoeEyxrE+−+−=rr c) Find the time-average power flow per unit area (magnitude and direction) carried by the following plane waves: i) ()()xjkoeEzyjrE−+=ˆˆrr ii) ()()( )[]yjkoeEjzjxrE 13ˆ2ˆ+++=rr iii) ()[]zjkoeHyjxrHˆˆ−=rr iv)
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