By Harry F. Tiersten
This tract is predicated on lecture notes for a direction in mechanics that has been provided at Rensselaer Polytechnic Institute off and on for the previous 20 years. The direction is meant to supply graduate scholars in mechanics with an knowing of electromagnetism and get ready them for reviews at the interplay of the electrical and magnetic fields with deformable good continua. As such, it truly is important that the excellence among particle and continuum descriptions of subject be conscientiously made and that the excellence among that that is inherently linear and that that's intrinsically nonlinear be in actual fact delineated. each attainable attempt has been made on my half to accomplish those ends. I desire to recognize the contributions of a couple of scholars and college who attended the lectures through the years and who, by means of their questions and proposals, considerably superior a number of the sections. This preface wouldn't be whole if i didn't indicate that my curiosity in electromagnetism used to be initiated and my angle in the direction of the advance of the equations was once encouraged by way of lectures given by means of the overdue Professor R.D. Mindlin at Columbia collage within the overdue nineteen fifties. i want to thank Professor C. Truesdell for his worthwhile feedback, which i believe considerably more desirable the readability and clarity of the creation, and Dr. M.G. Ancona for his remark in regards to the readability of a big aspect in Sec. 1.1.
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Additional info for A Development of the Equations of Electromagnetism in Material Continua
Formation of electric dipole moment from two point charges q(2) and q(3). self energy terms of the dipole in the same way, and for the same reason, that all terms containing such quantities as r11, r22, r33 etc. were ignored in the finite point charge case. This can be looked upon as redefining d/l so as to exclude the singular self energy of the point dipole. However, in this writer's view it is more appropriate and, indeed, more realistic to note that the point dipoles and point charges, from which the dipoles are defined, are only models which are convenient for developing the theory, as well as other purposes.
To this end we consider the electric field E (not the force on a unit point charge) in the neighborhood of two point charges + q and - q separated by the distance at, as shown in Figure 16, just as we did in the definition of polarization, and determine the force exerted by E on the two charges and then take the limit of the expression as 1-+ 0 and q -+ 00 while the product Iq -+ m. 2) and in the limit 1-+ 0, we may write E+ = E- + laoVE-. 3) Hence in the limit q-+ 00 we have f = lqaoVQEQ- = moVQEQ-.
2. In the point charge description the concept of a Maxwell electrostatic stress tensor defined at each point of space is meaningless and of no value whereas in the field description it is meaningful and has great value. 4) for the field energy to the problem of a cavity in a metal, where the cavity is a vacuum. A diagram of the configuration is shown in Figure 17. Since there can be no volumetric charge density in either the vacuum or the metal, it is clear that we can have only surface charge density on the metal-vacuum interface.
A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten