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 previous two decades. The path is meant to supply graduate scholars in mechanics with an realizing of electromagnetism and get ready them for experiences at the interplay of the electrical and magnetic fields with deformable stable continua. As such, it truly is relevant that the excellence among particle and continuum descriptions of subject be conscientiously made and that the excellence among that that is inherently linear and that that is 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 college who attended the lectures through the years and who, by means of their questions and proposals, considerably more desirable the various 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 used to be prompted through lectures given by means of the past due Professor R.D. Mindlin at Columbia college within the overdue nineteen fifties. i want to thank Professor C. Truesdell for his important feedback, which i believe considerably more suitable the readability and clarity of the advent, and Dr. M.G. Ancona for his remark in regards to the readability of an enormous element in Sec. 1.1.
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Extra resources for A Development of the Equations of Electromagnetism in Material Continua
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. 8) dF(PQ) #- - dF(QP). However, when the total force F P is determined by integrating over both complete current loops, we find that the law of action and reaction is satisfied for the interaction of the two complete circuits. 1) and integrating over both current loops to obtain F(PQ)= IPI Qf.
20) may be due to the entire Q circuit or any portion thereof. 21) for the electrostatic energy of a point charge at P in a potential cp resulting from other point charges at Q points or rather charge density. Let us now consider a system of current loops all distinct from each other and P as shown in Figure 22, and by superposition determine the magnetic induction vector B and vector potential A at P due to the elements of current of the loops at points QN. 23) 56 6. Magnetic Field Equations in Regions Carrying Steady Currents B(P) FIGURE 22.
13) which says that the resultant force acting between the two complete circuits is equal and opposite. 11), the forces due to the individual elements of circuit P can still result in a couple. However, since the resultant force vanishes, the moment of the force system due to an element of the Q circuit on the entire P circuit about any 52 6. 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.
A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten