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 earlier 20 years. The direction 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 good continua. As such, it really is principal that the excellence among particle and continuum descriptions of topic be rigorously made and that the excellence among that that is inherently linear and that that is intrinsically nonlinear be sincerely 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 way of their questions and recommendations, considerably stronger a few 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 was once prompted by means of lectures given by means of the overdue Professor R.D. Mindlin at Columbia college within the overdue nineteen fifties. i need to thank Professor C. Truesdell for his beneficial feedback, which i think considerably stronger the readability and clarity of the creation, and Dr. M.G. Ancona for his remark about the readability of a massive aspect in Sec. 1.1.
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Extra info for A Development of the Equations of Electromagnetism in Material Continua
1 The Magnetic Force Law Before we introduce the magnetic force law we should make a number of observations. Many of the older texts develop magnetostatics by defining magnetic point charges and introducing Coulomb's law for the magnetic charges, and developing magneto statics in direct analogy with electrostatics. This is obviously a very simple and straightforward approach. However, it is open to the following rather devastating criticisms: 1. , only the + and - charge in combination as the magnetic dipole moment has ever been found no matter how small the element of matter examined.
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. VE)dV. 9) arises from sources both inside and outside the region denoted V. 10) where f is the body force density or body force per unit volume, we have shown that the expression for f exerted by E on charged and polarized material continua may be written in the form f=pE+P·VE.
NPiCP +! i ] dV c¥t = -1 - D·· ----"-' cP - ~ 2 v 4n 4n + i v uL(P) dV. 3. 10) we obtain 011 = ~ r EiEi dV + r uL(P)dV. , when p, P and (J are present, the stored energy in the field and the matter is just the ordinary electrostatic energy of free space E 2 /8n and the local material energy of induced polarization plus the energy associated with the local field that has been left out in defining E. 22), which we have obtained, is perfectly general and is valid in the nonlinear case. p. E. P. 6) which is the well-known expression for the energy in linear electrostatics.
A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten