By Fabrizio Frezza
This publication is a concise creation to electromagnetics and electromagnetic fields that covers the elements of such a lot value for engineering functions through a rigorous, analytical therapy. After an creation to equations and uncomplicated theorems, subject matters of primary theoretical and applicative value, together with airplane waves, transmission strains, waveguides and Green's features, are mentioned in a intentionally normal method. Care has been taken to make sure that the textual content is instantly obtainable and self-consistent, with conservation of the intermediate steps within the analytical derivations. The ebook bargains the reader a transparent, succinct path in simple electromagnetic thought. it is going to even be an invaluable look up software for college students and designers.
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Extra resources for A Primer on Electromagnetic Fields
Once the Lorenz condition is met, the scalar potential can be expressed as a function of the vector potential: V = ∇·A , − jωεc and we can then express the electric field in terms of the only variable A: E = − jωμ A + ∇∇ · A . jωεc Let us consider finally the dual case in which Ji ≡ 0 and Jmi = 0. Then, applying the divergence to the second Maxwell’s equation it follows, again assuming the homogeneity of the medium: ∇·E =0 ⇒ E = −∇ × F where the minus sign has been introduced because F results the dual quantity of A, having: A→F , F → −A.
G. planes, cylinders, spheres) is used to name the wave (plane, cylindrical, spherical). The phase vector is defined as β = ∇ . It can be shown that, as for any gradient, its direction is the direction in which the phase variation is maximum; moreover β is orthogonal to equiphase surfaces; finally, obviously, β ≡ 0 for a standing wave. As it should be known, the superposition of two progressive waves having same module and of opposite phases generates a standing wave. To show this, let us write: A1 (x, y, z) = M(x, y, z) e− j (x,y,z) , A2 (x, y, z) = M(x, y, z) e j (x,y,z) , it follows: A1 (x, y, z) + A2 (x, y, z) = M(x, y, z) e j = 2 M(x, y, z) cos (x,y,z) + e− j (x,y,z) (x, y, z) , which is a real function.
Instead, the interpretation of the theorem which follows is valid only in harmonic regime, because it involves phasors formulas. We concentrate now, for example, on the term relevant to the flux of the Poynting n · E × H dS and we consider its average value on the vector in the time domain S 1 T t f (t) dt = f (t) for a generic function of T o time f (t). Assuming that the volume V and the surface S are at rest, we can reverse the integrals in space and time, and then carry on the mean operation on the product E(r, t) × H (r, t).
A Primer on Electromagnetic Fields by Fabrizio Frezza