A Development of the Equations of Electromagnetism in Material Continua

ISBN-13: 9781461396819 / Angielski / Miękka / 2012 / 158 str.

Harry F. Tiersten

Opis

This tract is based on lecture notes for a course in mechanics that has been offered at Rensselaer Polytechnic Institute on and off for the past twenty years. The course is intended to provide graduate students in mechanics with an understanding of electromagnetism and prepare them for studies on the interaction of the electric and magnetic fields with deformable solid continua. As such, it is imperative that the distinction between particle and continuum descriptions of matter be carefully made and that the distinction between that which is inherently linear and that which is intrinsically nonlinear be clearly delineated. Every possible effort has been made on my part to achieve these ends. I wish to acknowledge the contributions of a number of students and faculty who attended the lectures over the years and who, by their questions and suggestions, significantly improved some of the sections. This preface would not be complete if I did not point out that my interest in electromagnetism was initiated and my attitude towards the development of the equations was influenced by lectures given by the late Professor R.D. Mindlin at Columbia University in the late nineteen fifties. I would like to thank Professor C. Truesdell for his helpful suggestions, which I feel significantly improved the clarity and readability of the Introduction, and Dr. M.G. Ancona for his comment concerning the clarity of an important point in Sec. 1.1.

Spis treści

1. Introduction.- 1.1 General.- 1.2 Electrostatics.- 1.3 Magnetostatics.- 1.4 Electromagnetics.- I. Electrostatics.- 2. Electric Field Equations in Charged Regions.- 2.1 The Electric Field.- 2.2 Continuous Charge Distributions.- 2.3 Geometric Considerations.- 2.4 Fields Inside the Charged Region.- 2.5 Field Equation on Charge Density.- 3. Electric Field Equations in Charged and Polarized Regions.- 3.1 The Electric Dipole Moment.- 3.2 Fields Inside the Polarized Region.- 3.3 Field Equation of Electrostatics.- 3.4 Linearized Electrostatics.- 3.5 Boundary Conditions of Electrostatics.- 4. Forces and Torques Exerted by the Electric Field on Charged and Polarized Matter.- 4.1 Electric Body Forces.- 4.2 Maxwell Electrostatic Stress Tensor.- 4.3 Electric Torques.- 5. Electrostatic Energy.- 5.1 Energy Resulting from Distributions of Charge.- 5.2 Energy Resulting from Distributions of Charge and Polarization.- 5.3 Energy in Linear Electrostatics.- II. Magnetostatics.- 6. Magnetic Field Equations in Regions Carrying Steady Currents.- 6.1 The Magnetic Force Law.- 6.2 The Magnetic Induction Field.- 6.3 Continuous Distributions of Current.- 6.4 Field Equation on Current Density.- 7. Magnetic Field Equations in Magnetized Regions Carrying Steady Current.- 7.1 The Magnetic Dipole Moment.- 7.2 Fields Inside the Magnetized Region.- 7.3 Field Equation of Magnetostatics.- 7.4 Linearized Magnetostatics.- 7.5 Boundary Conditions of Magnetostatics.- 8. Forces and Torques Exerted by the Magnetic Induction Field on Magnetized Matter Carrying Current.- 8.1 Magnetic Body Forces.- 8.2 Maxwell Magnetostatic Stress Tensor.- 8.3 Magnetic Torques.- 9. Magnetostatic Energy.- 9.1 Energy Resulting from Distributions of Current.- 9.2 Energy Resulting from Distributions of Current and Magnetization.- 9.3 Energy in Linear Magnetostatics.- III. Electromagnetics.- 10. The Electromagnetic Field Equations.- 10.1 Time Dependence.- 10.2 Linearized Electromagnetism.- 10.3 Electromagnetism in Free-Space.- 10.4 Electromagnetic Boundary Conditions.- 11. Energy and Momentum in the Electromagnetic Field.- 11.1 Electromagnetic Energy.- 11.2 Electromagnetic Momentum and Force.- 12. The Influence of Motion on the Electromagnetic Field Equations.- 12.1 Boundary Conditions at Moving Surfaces of Discontinuity.- 12.2 Relative Motion and the Speed of Light.- 12.3 Transformation of the Electromagnetic Field Variables Resulting from Relative Motion.- 13. The Electromagnetic Potentials.- 13.1 The Electromagnetic Potential Formulation of Maxwell’s Equations.- 13.2 The Quasi-Static Electric Field.- 13.3 The Quasi-Static Magnetic Field for Insulators.- 14. Linear Circuit Equations from Maxwell’s Equations.- 14.1 Electric Circuit Equations and Voltage Generation.- 14.2 Capacitance and Resistance.- 14.3 Mutual and Self-Inductance.- 14.4 Parallel Circuits.- Footnotes and References.- Author Index.