329lect18 - 18 Wave equation and plane TEM waves in...

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18 Wave equation and plane TEM waves in source- free media With this lecture we start our study of the full set of Maxwell’s equations shown in the margin by Frst restricting our attention to homogeneous and non-conducting media with constant ± and μ and zero σ . ∇· D = ρ B =0 ∇× E = - B ∂t H = J + D . Our Frst objective is to show that non-trivial (i.e., non-zero) time- varying Feld solutions of these equations can be obtained even in the absence of ρ and J . We already know static ρ and J to be the source of static electric and magnetic Felds. We will come to understand that time varying ρ and J , which necessarily obey the continuity equation ∂ρ + J , constitute the source of time-varying electromagnetic Felds. Despite these intimate connections between the sources ρ and J and the Felds D = ± E and B = μ H , non-trivial feld solutions can exist in source-free media as we will see shortly. 1
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Such feld solutions in Fact represent electromagnetic waves, a Familiar example oF which is light . Another example is radiowaves that we use when we communicate using wireless devices such as radios, cell-phones, Wi±i, etc. Di²erent types oF electromagnetic waves are distinguished by their os- cillation Frequencies, and include radiowaves, microwaves, inFrared, light, ultraviolet, X-rays, and gamma rays, going across the electromagnetic spectrum From low to high Fre- quencies. We are well aware that these types oF electromagnetic waves can travel across empty regions oF space — e.g., From sun to Earth — transporting energy and heat as well as momentum. Next, we will discover their general properties by examining Maxwell’s equations under the restriction ρ = J =0 .
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This note was uploaded on 07/19/2010 for the course ECE ECE329 taught by Professor Kudeki during the Summer '10 term at University of Illinois at Urbana–Champaign.

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329lect18 - 18 Wave equation and plane TEM waves in...

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