By Harry F. Tiersten
This tract is predicated on lecture notes for a path in mechanics that has been provided at Rensselaer Polytechnic Institute off and on for the earlier two decades. The path is meant to supply graduate scholars in mechanics with an figuring out of electromagnetism and get ready them for experiences at the interplay of the electrical and magnetic fields with deformable reliable continua. As such, it really is critical that the excellence among particle and continuum descriptions of subject be rigorously made and that the excellence among that that is inherently linear and that that is intrinsically nonlinear be basically 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 school who attended the lectures through the years and who, by way of their questions and proposals, considerably more advantageous many of the sections. This preface wouldn't be entire if i didn't indicate that my curiosity in electromagnetism used to be initiated and my perspective in the direction of the advance of the equations used to be inspired by means of lectures given via the past due Professor R.D. Mindlin at Columbia collage within the overdue nineteen fifties. i need to thank Professor C. Truesdell for his precious feedback, which i believe considerably enhanced the readability and clarity of the advent, and Dr. M.G. Ancona for his remark in regards to the readability of an immense element in Sec. 1.1.
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Additional resources for A Development of the Equations of Electromagnetism in Material Continua
Example text
N)] + ... (1 + 1) + ... 6) 42 5. Electrostatic Energy Eq. 5) can be written in the form _1 ) rN2 + lq(N) [ L(1) + q(3)la'V 2 ( 2 which with rN1 (N - 1) ] + ... 7) , m(2) = q(3)la enables us to write ) + iq(N{ ::1: + m(2). V2C~2 + ... cX, it is clear that Eq. 6) for
The symbol X is called the electric susceptibility and Xij the susceptibility tensor. It is of second rank. 4) is the dielectric tensor. 6) D=sE, where s is called the dielectric constant. 7) as the scalar differential equation valid in each region with different sand p. This is a Poisson equation and to this we have to adjoin the boundary conditions. However, before we do this we observe that in actuality we have no particular interest in the linear constitutive equations we have written in this section, only in the development and the equations up through Sec.
In other words the point charges are foreigners to the field theory and the charge and polarization densities are not. 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.