Magnetic Fields, Special Relativity and Potential Theory

Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell's equations.
This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from electrostatics, magnetism, current flow, and gravitation. Relaxing the constraint of stationary steady currents, the next chapter considers electromagnetic induction when the current strengths in closed circuits vary or when the circuits move. This leads to the necessity of assessing the breakdown of Newtonian ideas and the introduction of special relativity. When the constraint of closed circuits is further relaxed and the motion of charges in open circuits is taken into account, the discussion turns to displacement current because of the relativistic theory already set up, leading to Maxwell's equations.
This book will be a valuable resource for undergraduate students of physics.

Contenu

Preface to Volume 2

6. Magnetostatics
   6.1 Introduction
   6.2 Origin of the Magnetic Field
   6.3 The Magnetic Displacement Vector
   6.4 Boundary Conditions
   6.5 The Magnetostatic Scalar Potential
   6.6 Small Magnets
   6.7 Inductance
7. Magnetization
   7.1 Permanent Magnets
   7.2 Permeable Media
   7.3 Induced Magnetization
   7.4 Hysteresis
8. Potential Problems
   8.1 Fundamental Theorems and Techniques
   8.2 The Method of Images
   8.3 Three-Dimensional Problems with Axial Symmetry
   8.4 Two-Dimensional Problems
   8.5 Gravitation
9. Electromagnetic Induction and Magnetic Energy
   9.1 Faraday's and Neumann's Law
   9.2 Observers in Motion: the Lorentz Transformation
   9.3 The Lorentz Transformation of Field Quantities
   9.4 The Lorentz Force on a Moving Charge
   9.5 Non-Steady Currents
   9.6 Initial Conditions: Switching
   9.7 Quasi-Steady Currents
   9.8 Magnetic Energy and Forces
   9.9 Dissipation of Energy by Quasi-Steady Currents
10. The Displacement Current and Maxwell's Equations
    10.1 The Displacement Current
    10.2 Electromagnetic Radiation
    10.3 Boundary Conditions at Discontinuities
    10.4 Pointing's Vector
    10.5 Maxwell's Stress Tensor and Electromagnetic Momentum
    Answers to the Exercises
    Index