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 previous 20 years. The direction is meant to supply graduate scholars in mechanics with an figuring out of electromagnetism and get ready them for reports at the interplay of the electrical and magnetic fields with deformable reliable continua. As such, it truly is relevant 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 basically 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 way of their questions and recommendations, considerably superior 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 angle in the direction of the improvement of the equations was once encouraged through lectures given by way of the overdue Professor R.D. Mindlin at Columbia collage within the past due nineteen fifties. i want to thank Professor C. Truesdell for his necessary feedback, which i think considerably stronger the readability and clarity of the advent, and Dr. M.G. Ancona for his remark in regards to the readability of a tremendous element in Sec. 1.1.
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Additional resources for A Development of the Equations of Electromagnetism in Material Continua
We are assuming a right-handed coordinate system throughout. In the equation of definition we have assumed that we have a point charge qQ moving with a velocity yQ. 5) 54 6. 11), we have wQ at Q. 9) (V P)2 A = 0, except at Q. 10) Although we cannot define the energy of a magnetostatic system by considering moving elements of charge in which the law of action and reaction is not satisfied, we can define the energy for a magnetostatic system by considering steady currents flowing in closed loops.
Magnetic Field Equations in Regions Carrying Steady Currents FIGURE 21. Schematic diagram showing element of Q circuit and entire P circuit. point is the same. 11) and the diagram in Figure 21 is the point of the fixed element ds Q of the source. 15) CP '1 in which we have defined the s coordinate as the distance from s~ along the curve of the P circuit and we have replaced d'l by ds since they are identical. 15) in the form dC = _1. 16) since FR and FS are single-valued. 11) due to any given element ds Q of the Q circuit acting on the entire P circuit vanishes as well as the force.
2. The Magnetic Induction Field 55 where di represents the arbitrary infinitesimal rigid translation of the P circuit relative to the Q circuit. 11) we obtain VPV = IPIQ1. 1. 16) where F (PQ) is the resultant force exerted by current loop Q on current loop P. The quantity U Vi we identify the magnetostatic energy since its translational gradient with respect to the P points yields the force F (PQ), which is exerted by current loop Q on current loop P. 20) may be due to the entire Q circuit or any portion thereof.
A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten