By Fabrizio Frezza
This ebook is a concise creation to electromagnetics and electromagnetic fields that covers the points of so much value for engineering purposes via a rigorous, analytical therapy. After an advent to equations and easy theorems, subject matters of primary theoretical and applicative value, together with aircraft waves, transmission strains, waveguides and Green's features, are mentioned in a intentionally common means. Care has been taken to make sure that the textual content is quickly obtainable and self-consistent, with conservation of the intermediate steps within the analytical derivations. The e-book deals the reader a transparent, succinct direction in uncomplicated electromagnetic concept. it's going to even be an invaluable search for software for college students and designers.
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Extra resources for A Primer on Electromagnetic Fields
6 In the anisotropic case (still non-dispersive) we have: pc = 1 (σ · E ∗ ) · E. 2 In order to find the conditions under which this quantity is real, let’s consider first the more general case of a dispersive anisotropic medium, in which the tensor σ is in general complex. We then have: pc = 1 ∗ ∗ (σ · E ) · E. , developing the scalar products: 3 3 Ei i=1 j=1 σij∗ E ∗j − 3 j=1 3 3 E ∗j 3 σji E i = i=1 (σij∗ − σji ) E i E ∗j = 0. i=1 j=1 The previous relation must be valid for any electric field propagating in that medium.
So the theorem is demonstrated, even if the medium is not dissipative ( pcd ≡ 0 being σ = 0). 2 Uniqueness Theorem in the Frequency Domain We are now going to use the complex Poynting’s theorem to derive the uniqueness theorem in the frequency domain. In this case, having eliminated the time dependence, there are no initial conditions but only boundary conditions. Referring to the usual volume V enclosed by a closed surface S and with outward normal unit vector n, it is unique in any point of V the electromagnetic field which is solution of Maxwell’s equations and constitutive relations, and whose is assigned in any point of S either the tangential component of the electric field or the tangential component of the magnetic field.
The previous relation, called separability condition, should be imposed to ensure that the three equations of harmonic motions are equivalent to the initial equation. In particular, the three constants k x , k y and k z can not be simultaneously zero, being k 2 = ω 2 μεc = 0. Let us now examine the first equation: d2 X + k x2 X = 0 . dx2 The general solution is obtained considering separately the two cases k x = 0 and k x = 0. We have in the first case: X (x) = X o+ e−jkx x + X o− ejkx x , with X o+ and X o− arbitrary complex constants.