By Fabrizio Frezza
This e-book is a concise advent to electromagnetics and electromagnetic fields that covers the facets of such a lot value for engineering functions by way of a rigorous, analytical remedy. After an advent to equations and easy theorems, issues of primary theoretical and applicative value, together with aircraft waves, transmission traces, waveguides and Green's capabilities, are mentioned in a intentionally common means. Care has been taken to make sure that the textual content is instantly available and self-consistent, with conservation of the intermediate steps within the analytical derivations. The e-book bargains the reader a transparent, succinct direction in easy electromagnetic conception. it's going to even be an invaluable look up software for college kids and designers.
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Extra resources for A Primer on Electromagnetic Fields
The equation M(x, y, z) = constant defines, if not identically verified, a family of surfaces which are called equi-amplitude surfaces. A wave is said to be uniform (more often referred in the literature as homogeneous) if the amplitude is constant on the equiphase surfaces. This occurs, either when the previous relation is identically verified, or when the equi-amplitude surfaces coincide with equiphase surfaces. Returning now to the time domain, in monochromatic regime we have: A(x, y, z, t) = Re A(x, y, z) e jωt = M(x, y, z) cos ωt − (x, y, z) .
In order to determine the equiphase surfaces, let us observe that if the two points P and P , identified by the vectors r and r , belong to an equiphase surface, then it must be (r ) = (r ), and therefore: β·r = β·r ⇒ β·(r − r ) = 0 . e. it must lie on a plane orthogonal to β. We conclude that the equiphase surfaces are planes normal to β and defined by the equation β·r = constant. Our solution is therefore a plane wave. The direction of the vector β is called direction of propagation. Similarly, the equi-amplitude surfaces are planes normal to α.
In this case, the determinant of the matrix itself and all the eigenvalues are real numbers (recall the general property which states that the determinant is the product of the eigenvalues, each taken with its multiplicity). As we have already seen, if the matrix is Hermitian, whatever the values of the variables are (in our case, the components of the fields), the value assumed by the form is always real, and viceversa. Furthermore, it is shown that a necessary and sufficient condition for the Hermitian form to be defined positive (which is important for us for physical reasons when we consider the dissipated power and the energy density) is that the (real) eigenvalues of the matrix are all positive.
A Primer on Electromagnetic Fields by Fabrizio Frezza