By A. Cemal Eringen, Gerard A. Maugin
The electrodynamics of continua is a department ofthe actual sciences eager about the interplay of electromagnetic fields with deformable our bodies. De formable our bodies are thought of to be continua endowed with non-stop distributions of mass and cost. the speculation of electromagnetic continua is worried with the decision of deformations, motions, rigidity, and elec tromagnetic fields built in our bodies upon the purposes of exterior a lot. exterior quite a bit could be of mechanical foundation (e.g., forces, undefined, constraints put on the outside of the physique, and preliminary and boundary stipulations coming up from thermal and different alterations) and/or electromagnetic foundation (e.g., electrical, magnetic, and present fields). simply because our bodies of alternative constitutions reply to exterior stimuli otherwise, it's valuable to signify effectively the reaction capabilities suitable to a given classification of continua. this is often performed by way of the constitutive conception. for instance, an elastic dielectric responds to electromagnetic fields in a wholly diverse approach than a magnetic fluid. the current ebook is meant to offer a unified method of the subject material, according to the foundations of up to date continuum physics.
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Additional info for Electrodynamics of Continua I: Foundations and Solid Media
In a natural way, this leads to the notion of macroscopic concepts such as polarization, magnetization, charge, and current, and their expressions in terms of microscopic notions. 4, which leads to the introduction of fields expressed in a moving frame of reference. 5 we obtain expressions for the macroscopic densities of mass, force, couple, and power by means of the statistical averaging procedure. The coupling of the electromagnetic fields to the mechanical field can only be provided when these expressions are found.
23) This formula remains valid when ~ is a tensor field. 16 Finally, we set forth the following useful definition: Definition. The line integral of the tangential component of a vector field q along a curve c is called its circulation. Thus, r(q) = t q. dx. 25) (V x q)·da, where s is any surface bounded by c. This is stated as: the circulation of q around a closed circuit is equal to the flux of V x q through any surface bounded by the circuit. The notion of circulation plays a prominent role in both electromagnetism and fluid dynamics.
X'" V)J(x" - x). 13) 1. 10), we obtain 1 ae c at V x b - - - = -J 1 ap c at + -- + V x m, where we introduced the abbreviations mIX . n L e"P L ~"P x ~"P(~"P. Vr J(x" c " (n + 1)! 1 1
Electrodynamics of Continua I: Foundations and Solid Media by A. Cemal Eringen, Gerard A. Maugin