A Development of the Equations of Electromagnetism in Material Continua

1. Front Matter

   Pages i-xi

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2. Introduction

   1. Introduction

      • Harry F. Tiersten

      Pages 1-6

3. Electrostatics

   1. Front Matter

      Pages 7-7

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   2. Electric Field Equations in Charged Regions

      • Harry F. Tiersten

      Pages 9-20

   3. Electric Field Equations in Charged and Polarized Regions

      • Harry F. Tiersten

      Pages 21-31

   4. Forces and Torques Exerted by the Electric Field on Charged and Polarized Matter

      • Harry F. Tiersten

      Pages 32-36

   5. Electrostatic Energy

      • Harry F. Tiersten

      Pages 37-46

4. Magnetostatics

   1. Front Matter

      Pages 47-47

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   2. Magnetic Field Equations in Regions Carrying Steady Currents

      • Harry F. Tiersten

      Pages 49-61

   3. Magnetic Field Equations in Magnetized Regions Carrying Steady Current

      • Harry F. Tiersten

      Pages 62-72

   4. Forces and Torques Exerted by the Magnetic Induction Field on Magnetized Matter Carrying Current

      • Harry F. Tiersten

      Pages 73-79

   5. Magnetostatic Energy

      • Harry F. Tiersten

      Pages 80-91

5. Electromagnetics

   1. Front Matter

      Pages 93-93

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   2. The Electromagnetic Field Equations

      • Harry F. Tiersten

      Pages 95-104

   3. Energy and Momentum in the Electromagnetic Field

      • Harry F. Tiersten

      Pages 105-112

   4. The Influence of Motion on the Electromagnetic Field Equations

      • Harry F. Tiersten

      Pages 113-129

   5. The Electromagnetic Potentials

      • Harry F. Tiersten

      Pages 130-136

   6. Linear Circuit Equations from Maxwell’s Equations

      • Harry F. Tiersten

      Pages 137-145

6. Back Matter

   Pages 146-158

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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.

• Potential
• applied mathematics
• electromagnetic field
• electromagnetism
• magnetic field
• magnetism
• mechanics

• Department of Mechanical Engineering, Aeronautical Engineering & Mechanics, Rensselaer Polytechnic Institute, Troy, USA

  Harry F. Tiersten

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