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 two decades. The path 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 stable continua. As such, it's primary 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 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, by means of their questions and recommendations, considerably better a few 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 advance of the equations was once motivated via lectures given via the past due Professor R.D. Mindlin at Columbia collage within the overdue nineteen fifties. i want to thank Professor C. Truesdell for his valuable feedback, which i think considerably enhanced 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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Additional resources for A Development of the Equations of Electromagnetism in Material Continua
18) along similar lines so as to account for what might well be called the finite portion of the magnetic self energy of a loop. This will be discussed in greater detail later on when we discuss the magnetic field energy of a collection of loops. We now proceed to replace the discrete current elements wIn), which must, of course, be portions of loops, by a variable distribution of current density J, which may have discontinuities at points, lines and surfaces. This replacement takes place in exactly the same manner that the q(n) were replaced 58 6.
In other words the direction of B depends on whether the coordinate system is left or right handed. 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.
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. System of elements of current loops. 24) at each point P not occupied by current elements. 3 V·B=O except at each Q(n). 25) Continuous Distributions of Current Before proceeding with a discussion of continuous distributions of current it should be noted that when we write the expression for A and B as sums over current elements wIn), rather than sums over current loop integrals around C
A Development of the Equations of Electromagnetism in Material Continua by Harry F. Tiersten