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ps1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Problem Set No. 1 6.630 Electromagnetic Theory Issued: Week 1 Fall Term 2006 Due: Week 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Reading assignment : Section 1.1-1.2 ; J. A. Kong, “ Electromagnetic Wave Theory ,” EMW, 2005. Problem P1.1 An electromagnetic wave has spatial frequency k o = 100 K o . Determine the wavelength in meters and the temporal frequency in GHz. Determine the spatial frequency in units of K o for a laser light at wavelength λ = 0 . 350 μ m . Determine the spatial frequency in units of K o for a microwave oven at frequency 2.45 GHz. Problem P1.2 Electromagnetic waves satisfy all of the Maxwell equations. Consider, in free space, the following electric field vectors: E 1 = ˆ z cos( ω t - kz ) E 2 = (ˆ x + ˆ z ) cos ω t + k | x - z | / 2 E 3 = (ˆ x + ˆ z ) cos( ω t + ky ) (a) Do these electric field vectors satisfy the wave equation 2 - μ o o 2 t 2 E = 0 What is the relationship between ω and k ?

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