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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 prior two decades. The direction is meant to supply graduate scholars in mechanics with an realizing of electromagnetism and get ready them for stories at the interplay of the electrical and magnetic fields with deformable stable continua. As such, it's central that the excellence among particle and continuum descriptions of topic be conscientiously made and that the excellence among that that is inherently linear and that that's 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, through their questions and proposals, considerably more advantageous many of the sections. This preface wouldn't be whole if i didn't indicate that my curiosity in electromagnetism was once initiated and my angle in the direction of the advance of the equations used to be motivated via lectures given by way of the overdue Professor R.D. Mindlin at Columbia college within the past due nineteen fifties. i need to thank Professor C. Truesdell for his important feedback, which i think considerably enhanced the readability and clarity of the advent, and Dr. M.G. Ancona for his remark in regards to the readability of a major aspect in Sec. 1.1.

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5. 14) where t denotes an arbitrary unit vector lying in s. 15) N, where N denotes a unit vector normal to the curve C and lying in s. Then we have i (E + - E -). 17) for any line element 1 on s and any accompanying N, including in particular any arbitrary infinitesimall and the associated N. 18) as the condition on E across a discontinuity surface S. 19) which says that the tangential component of E is continuous across any surface of discontinuity. Moreover, since in electrostatics E = - V({J, the tangential components of E are determined by the surface gradient of ({J, which is determined by the values of ({J at each point of the surface, and we have the equivalent condition [({J] = K across S, where K is at most a constant, which is physically irrelevant.

Interior dielectric in a metal. f acpdS+! 13) where uL is included, in accordance with our discussion, in order to account for the local electrical energy of induced polarization and Lorentz local field, which is not included in E. The boundary conditions at the metal-vacuum interface are given by Eqs. 18) Substituting in the expression for c¥t and dropping the -, we obtain c¥t = - ~f 8n s 2Jrv (pcp + PiCP,;)dV + f v uL(P)dV. nPiCP +! i ] dV c¥t = -1 - D·· ----"-' cP - ~ 2 v 4n 4n + i v uL(P) dV.

5) n=1 Then we note that for the microscopic region of interest, which enables us to define the macroscopic polarization density P, the gradient of the macroscopic electric field has one value. Consequently, for a region of that size Eq. 5) may be written in the form f= M L m(n)·VE. 7), we may write dF=P·VEdV. 7) the expression for the force exerted by the electric field on continuous distributions of charge density p and polarization P in a differential element of volume dV may be written in the form dF = (pE + p.

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