By Harry F. Tiersten

ISBN-10: 1461396794

ISBN-13: 9781461396796

ISBN-10: 1461396816

ISBN-13: 9781461396819

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 20 years. The path is meant to supply graduate scholars in mechanics with an knowing 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 crucial that the excellence among particle and continuum descriptions of topic be conscientiously made and that the excellence among that that's inherently linear and that that is intrinsically nonlinear be truly 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, via 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 was once motivated by way of lectures given via the overdue Professor R.D. Mindlin at Columbia college within the past due nineteen fifties. i need to thank Professor C. Truesdell for his beneficial feedback, which i believe considerably more suitable the readability and clarity of the creation, and Dr. M.G. Ancona for his remark in regards to the readability of a huge aspect in Sec. 1.1.

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Additional resources for A Development of the Equations of Electromagnetism in Material Continua

Example text

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. 3. 10). 1 0) can be written in the equivalent form v x E=O.

However, before proceeding with the development we must say something about the magnetic units in which we will work. 3) gives us the electromagnetic unit of electric charge and this differs from the electrostatic unit of electric charge both dimensionally and numerically. u. u. 3) we already have [qe] =L3/2Ml/2T-l =~(ML)1/2. 1. The Magnetic Force Law 51 which shows that the ratio is a velocity. Moreover, measurement shows that this velocity is the speed of light c = 3 X 10 10 em/sec. u. of current corresponds to 10 amps.

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.

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A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten


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