By James Clerk Maxwell

ISBN-10: 1579100155

ISBN-13: 9781579100155

An unabridged, unaltered version in seven elements, to incorporate: Introductory - On Electromagnetic Induction - basic Equations of the Electromagnetic box - Mechanical activities within the box - conception of Condensers - Electromagnetic concept of sunshine - Calculation of the Coefficients of Electromagnetic Induction

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In this ®gure, since we are testing the numerical accuracy of the computation formulae, we let PBOX ˆ POUT ‡ PDE ‡ PDM ‡ j…ÀPWE ‡ PWM † and compare PIN and PBOX . As can be seen from Fig. 14, the real and imaginary parts of PIN (cross) and PBOX Copyright © 2000 Marcel Dekker, Inc. 52 Chapter 2 Figure 14 Plots of the real and imaginary parts of the complex Poynting theorem terms as results from Eqs. 21±27 given the same Poynting box as was used in Figs. 12 and 13 are shown. (solid line) are numerically indistinguishable from one another, showing that the numerical computations have been carried out accurately.

We may demonstrate that Vn eqn y is a solution of Eq. 8 by direct substitution. We have for n ˆ 1; 2, …d=dy†…Vn eqn y † ˆ Vn …d=dy†eqn y ˆ qn Vn eqn y . But qn Vn ˆ AVn , hence d …V eqn y † ˆ A…Vn eqn y † dy n …2:2:9† which is the original equation. Superposition of the distinct modes of Vn eqn y then gives the full EM solution. The eigenvalues of qn , n ˆ 1; 2; of A in Eq. 7 satisfy det‰A À qIŠ ˆ …Àq†2 À …j 2  † ˆ 0 Copyright © 2000 Marcel Dekker, Inc. Spectral State Variable Formulation 23 or q2 ‡   ˆ 0 …2:2:10† Let  ‡ j  q1 , > 0, > 0 ( and are real numbers), be the forward traveling mode in the ` ˆ 1; 2; 3 regions.

6 State Variable Analysis of a Source in Isotropic Layered Media In this subsection we consider the state variable analysis of the EM ®elds 3 that are excited when a planar sheet of electric surface current J S ˆ Jsx a” x ˆ J a” x (Amp/m) is located in the interior of an isotropic two-layered medium. Copyright © 2000 Marcel Dekker, Inc. Spectral State Variable Formulation 37 Figure 6 Plots of the various normalized power terms associated with the complex Poynting theorem of Eq. 34. This ®gure uses the same geometry as Fig.

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