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Electromagnetic Field Theory: A Problem Solving Approach Part 56

Electromagnetic Field Theory: A Problem Solving Approach Part 56. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Normal Incidence onto a Dielectric 525 We can easily explore the effect of losses in the low and large loss limits. a Low Losses If the Ohmic conductivity is small we can neglect it in all terms except in the wavenumber k2 lim 10 The imaginary part of k2 gives rise to a small rate of exponential decay in medium 2 as the wave propagates away from the z 0 boundary. b Large Losses For large conductivities so that the displacement current is negligible in medium 2 the wavenumber and impedance in region 2 are complex lim 8 o ju.2cr litom i y 172 V------- V r ao ID The fields decay within a characteristic distance equal to the skin depth 8. This is why communications to submerged submarines are difficult. For seawater M2 Mo 4tt X 10-7 henry m and cr 4 siemens m so that for 1 MHz signals 5 0.25 m. However at 100 Hz the skin depth increases to 25 meters. If a submarine is within this distance from the surface it can receive the signals. However it is difficult to transmit these low frequencies because of the large free space wavelength A 3xl06m. Note that as the conductivity approaches infinity 2 00 -1 lim r- oo I 7J2 0 I T 0 12 so that the field solution approaches that of normal incidence upon a perfect conductor found in Section 7-5. EXAMPLE 7-1 DIELECTRIC COATING A thin lossless dielectric with permittivity e and permeability pc is coated onto the interface between two infinite halfspaces of lossless media with respective properties ej p.i and e2 7 2 . as shown in Figure 7-15. What coating parameters e and n and thickness d will allow all the time-average power 526 Electrodynamics Fields and Waves No reflections if d 1 3 5. . . 4 and v y j n t where X is Veju measured within the coating Figure 7-15 A suitable dielectric coating applied on the interface of discontinuity between differing media can eliminate reflections at a given frequency. from region 1 to be transmitted through the coating to region 2 Such coatings are applied to optical components such as lenses to .