ps4 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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------------------------------------------------------------------------------ MASSACHUSETTS INSTITUTE OF TECHNOLOGY± Department of Electrical Engineering and Computer Science± Problem Set No. 4 6.630 Electromagnetics Issued: Fall Term 2006 Due: Reading assignment : Section 1.5-1.6; J. A. Kong, “ Electromagnetic Wave Theory ,” EMW,± 2005.± Additional materials : Hertian dipole MATLAB scripts Problem P4.1 y z φ y z φ θ q 0 q z q y x x (a) (b) Fig.1 For a z -oriented dipole (Fig.1 a) the far field expression of E and H are: ˆ ˆ E = θk 2 q 0 cos( kr ωt ) sin θ H = φωkq 0 cos( kr ωt ) sin θ 4 πr 0 4 πr Consider two identical dipoles oriented as shown in Fig.1 (b). (a) What is the far field expression for E-field on the x y plane in the first quadrant? (b) What is the time average Poynting power at φ = 0 on the x y plane? Problem P4.2 Two Hertzian dipole antennas are located at (0 , 0 , 0) and (0 , d, 0) with dipole moments p 1 = q 1 l and p 2 = q 2 l as shown in Figure 2. The two in phase dipoles are oriented in z and x direction respectively.
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