By Harry F. Tiersten
This tract is predicated on lecture notes for a direction in mechanics that has been provided at Rensselaer Polytechnic Institute off and on for the prior 20 years. The direction is meant to supply graduate scholars in mechanics with an knowing of electromagnetism and get ready them for reviews at the interplay of the electrical and magnetic fields with deformable sturdy continua. As such, it truly 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's intrinsically nonlinear be in actual fact 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, through their questions and proposals, considerably stronger many 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 stimulated by means of lectures given by means of the past due 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 advent, and Dr. M.G. Ancona for his remark about the readability of a huge element in Sec. 1.1.
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Additional info for A Development of the Equations of Electromagnetism in Material Continua
11). It should be noted that in just about all practical situations, there is no charge density p in an insulator as well as in a conductor, and as a consequence, there is no surface charge at a dielectric-dielectric interface or at a conductor (metal)-conductor interface. Clearly then, the normal component of D is continuous across these interfaces. However, there almost always is a surface charge and, hence, a discontinuity in 0 D across a dielectric-conductor interface. 91- vanish so that the length I of s remains finite in the limit.
1). 1 Energy Resulting from Distributions of Charge This brings us to a consideration of electrostatic energy. , by considering the energy associated with a collection of point charges q(n). We first bring the first charge q(1) to a position and no work is done. Then we bring another charge from CIJ to its position and we determine the potential energy due to it as the negative of the work done by the field (or the work done on the field) in bringing it from CIJ to its position in the presence of 1.
This ends our development of electrostatics and brings us to magnetostatics. 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.
A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten