By Harry F. Tiersten
This tract relies on lecture notes for a path in mechanics that has been provided at Rensselaer Polytechnic Institute off and on for the prior two decades. The direction is meant to supply graduate scholars in mechanics with an realizing of electromagnetism and get ready them for reviews at the interplay of the electrical and magnetic fields with deformable reliable continua. As such, it really is vital 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 essentially delineated. each attainable attempt has been made on my half to accomplish those ends. I desire to recognize the contributions of a few scholars and college who attended the lectures through the years and who, by means of their questions and proposals, considerably more advantageous 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 perspective in the direction of the improvement of the equations used to be encouraged by means of lectures given by means of the past due Professor R.D. Mindlin at Columbia college within the past due nineteen fifties. i want to thank Professor C. Truesdell for his valuable feedback, which i think considerably better the readability and clarity of the advent, and Dr. M.G. Ancona for his remark in regards to the readability of a huge element in Sec. 1.1.
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Extra resources for A Development of the Equations of Electromagnetism in Material Continua
16 At this point it is purposeful to note that if an electric field E exists at points of free-space, the associated Maxwell electrostatic stress tensor TE exists. Both fields exist at the point in question independent of the location and values of the sources which generated E, which may not even be known. 16) 36 4. 17) in free space. 3 Electric Torques At this point it should be noted that in general TE is not symmetric. 1) and (TE)A will not be zero if P and E are not colinear. This means in essence that the electric field E can exert a couple on the polarization P, and that the Cauchy mechanical stress tensor cannot be expected to be symmetric in general when coupling with the electric field exists.
However, the differential form is required to obtain the field theory. 17) and eventually when the currents are not steady in closed loops. The fact that this form does not satisfy the law of action and reaction by itself does not deter us because, as we have seen, in the case of steady currents, which must flow in closed loops, the resultant forces between entire circuits does satisfy the law of action and reaction and in the nonsteady case we have time varying magnetic (and electric fields) and as we shall see later in electromagnetism the electromagnetic field carries linear momentum (even in free space).
11) in Gaussian units. Now, as you will recall, we have consistently used the point charge approach because of its physical clarity simply to motivate the field theory, and once the field theory has been obtained we have abandoned the point charge approach and generalized the field theory in a physically sensible way. We proceed with the same approach here also, but now in a somewhat bolder manner. , is a physical fact. This means that we associate with each volume element of free-space (or vacuum) in which an electric field e~ists an electric field energy density of E 2 /8n.