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 first 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 t . Our first objective is to show that non-trivial (i.e., non-zero) time- varying field 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 fields. We will come to understand that time varying ρ and J , which necessarily obey the continuity equation ∂ρ t + · J = 0 , constitute the source of time-varying electromagnetic fields. Despite these intimate connections between the sources ρ and J and the fields D = E and B = μ H , non-trivial field solutions can exist in source-free media as we will see shortly. 1
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Such field 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, WiFi, etc. Di ff erent 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.
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