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Electromagnetism: Maxwell Equations, Wave Propagation and Emission

Book Description

This book deals with electromagnetic theory and its applications at the level of a senior-level undergraduate course for science and engineering. The basic concepts and mathematical analysis are clearly developed and the important applications are analyzed. Each chapter contains numerous problems ranging in difficulty from simple applications to challenging. The answers for the problems are given at the end of the book. Some chapters which open doors to more advanced topics, such as wave theory, special relativity, emission of radiation by charges and antennas, are included.

The material of this book allows flexibility in the choice of the topics covered. Knowledge of basic calculus (vectors, differential equations and integration) and general physics is assumed. The required mathematical techniques are gradually introduced. After a detailed revision of time-independent phenomena in electrostatics and magnetism in vacuum, the electric and magnetic properties of matter are discussed. Induction, Maxwell equations and electromagnetic waves, their reflection, refraction, interference and diffraction are also studied in some detail. Four additional topics are introduced: guided waves, relativistic electrodynamics, particles in an electromagnetic field and emission of radiation. A useful appendix on mathematics, units and physical constants is included.

Contents

1. Prologue.

2. Electrostatics in Vacuum.

3. Conductors and Currents.

4. Dielectrics.

5. Special Techniques and Approximation Methods.

6. Magnetic Field in Vacuum.

7. Magnetism in Matter.

8. Induction.

9. Maxwell's Equations.

10. Electromagnetic Waves.

11. Reflection, Interference, Diffraction and Diffusion.

12. Guided Waves.

13. Special Relativity and Electrodynamics.

14. Motion of Charged Particles in an Electromagnetic Field.

15. Emission of Radiation.

Table of Contents

  1. Coverpage
  2. Titlepage
  3. Copyright
  4. Table of Contents
  5. Preface
  6. List of Symbols
  7. Chapter 1. Prologue
    1. 1.1. Scalars and vectors
    2. 1.2. Effect of rotations on scalars and vectors
    3. 1.3. Integrals involving vectors
    4. 1.4. Gradient and curl, conservative field and scalar potential
    5. 1.5. Divergence, conservative flux, and vector potential
    6. 1.6. Other properties of the vector differential operator
    7. 1.7. Invariance and physical laws
    8. 1.8. Electric charges in nature
    9. 1.9. Interactions in nature
    10. 1.10. Problems
  8. Chapter 2. Electrostatics in Vacuum
    1. 2.1. Electric forces and field
    2. 2.2. Electric energy and potential
    3. 2.3. The two fundamental laws of electrostatics
    4. 2.4. Poisson’s equation and its solutions
    5. 2.5. Symmetries of the electric field and potential
    6. 2.6. Electric dipole
    7. 2.7. Electric field and potential of simple charge configurations
    8. 2.8. Some general properties of the electric field and potential
    9. 2.9. Electrostatic energy of a system of charges
    10. 2.10. Electrostatic binding energy of ionic crystals and atomic nuclei
    11. 2.11. Interaction-at-a-distance and local interaction*
    12. 2.12. Problems
  9. Chapter 3. Conductors and Currents
    1. 3.1. Conductors in equilibrium
    2. 3.2. Conductors with cavities, electric shielding
    3. 3.3. Capacitors
    4. 3.4. Mutual electric influence of conductors
    5. 3.5. Electric forces between conductors
    6. 3.6. Currents and current densities
    7. 3.7. Classical model of conduction, Ohm’s law and the Joule effect
    8. 3.8. Resistance of conductors
    9. 3.9. Variation of resistivity with temperature, superconductivity
    10. 3.10. Band theory of conduction, semiconductors*
    11. 3.11. Electric circuits
    12. 3.12. Problems
  10. Chapter 4. Dielectrics
    1. 4.1. Effects of dielectric on capacitors
    2. 4.2. Polarization of dielectrics
    3. 4.3. Microscopic interpretation of polarization
    4. 4.4. Polarization charges in dielectric
    5. 4.5. Potential and field of polarized dielectrics
    6. 4.6. Gauss’s law in the case of dielectrics, electric displacement
    7. 4.7. Electrostatic equations in dielectrics
    8. 4.8. Field and potential of permanent dielectrics
    9. 4.9. Polarization of a dielectric in an external field
    10. 4.10. Energy and force in dielectrics
    11. 4.11. Action of an electric field on a polarized medium
    12. 4.12. Electric susceptibility and permittivity
    13. 4.13. Variation of polarization with temperature
    14. 4.14. Nonlinear dielectrics and non-isotropic dielectrics
    15. 4.15. Problems
  11. Chapter 5. Special Techniques and Approximation Methods
    1. 5.1. Unicity of the solution
    2. 5.2. Method of images
    3. 5.3. Method of analytic functions
    4. 5.4. Method of separation of variables
    5. 5.5. Laplace’s equation in Cartesian coordinates
    6. 5.6. Laplace’s equation in spherical coordinates
    7. 5.7. Laplace’s equation in cylindrical coordinates
    8. 5.8. Multipole expansion
    9. 5.9. Other methods
    10. 5.10. Problems
  12. Chapter 6. Magnetic Field in Vacuum
    1. 6.1. Force exerted by a magnetic field on a moving charge
    2. 6.2. Force exerted by a magnetic field on a current, Laplace’s force
    3. 6.3. Magnetic flux and vector potential
    4. 6.4. Magnetic field of particles and currents, Biot-Savart’s law
    5. 6.5. Magnetic moment
    6. 6.6. Symmetries of the magnetic field
    7. 6.7. Ampère’s law in the integral form
    8. 6.8. Field and potential of some simple circuits
    9. 6.9. Equations of time-independent magnetism in vacuum, singularities of B
    10. 6.10. Magnetic energy of a circuit in a field B
    11. 6.11. Magnetic forces
    12. 6.12. Question of magnetic monopoles*
    13. 6.13. Problems.
  13. Chapter 7. Magnetism in Matter
    1. 7.1. Types of magnetism
    2. 7.2. Diamagnetism and paramagnetism
    3. 7.3. Magnetization current
    4. 7.4. Magnetic field and vector potential in the presence of magnetic matter
    5. 7.5. Ampère’s law in the integral form in the presence of magnetic matter
    6. 7.6. Equations of time-independent magnetism in the presence of matter
    7. 7.7. Discontinuities of the magnetic field
    8. 7. 8. Examples of calculation of the field of permanent magnets
    9. 7.9. Magnetization of a body in an external field
    10. 7.10. Magnetic susceptibility, nonlinear mediums and non-isotropic mediums
    11. 7.11. Action of a magnetic field on a magnetic body
    12. 7.12. Magnetic energy in matter
    13. 7.13. Variation of magnetization with temperature
    14. 7.14. Ferromagnetism
    15. 7.15. Magnetic circuits
    16. 7.16. Problems
  14. Chapter 8. Induction
    1. 8.1. Induction due to the variation of the flux, Faraday’s and Lenz’s laws
    2. 8.2. Neumann’s induction
    3. 8.3. Lorentz induction
    4. 8.4. Lorentz induction and the Galilean transformation of fields
    5. 8.5. Mutual inductance and self-inductance
    6. 8.6. LR circuit
    7. 8.7. Magnetic energy
    8. 8.8. Magnetic forces acting on circuits
    9. 8.9. Some applications of induction
    10. 8.10. Problems
  15. Chapter 9. Maxwell’s Equations
    1. 9.1. Fundamental laws of electromagnetism
    2. 9.2. Maxwell’s equations
    3. 9.3. Electromagnetic potentials and gauge transformation
    4. 9.4. Quasi-permanent approximation
    5. 9.5. Discontinuities on the interface of two mediums
    6. 9.6. Electromagnetic energy and Poynting vector
    7. 9.7. Electromagnetic pressure, Maxwell’s tensor
    8. 9.8. Problems
  16. Chapter 10. Electromagnetic Waves
    1. 10.1. A short review on waves
    2. 10.2. Electromagnetic waves in infinite vacuum and dielectrics
    3. 10.3. Polarization of electromagnetic waves
    4. 10.4. Energy and intensity of plane electromagnetic waves
    5. 10.5. Momentum and angular momentum densities, radiation pressure
    6. 10.6. A simple model of dispersion
    7. 10.7. Electromagnetic waves in conductors
    8. 10.8. Electromagnetic waves in plasmas
    9. 10.9. Quantization of electromagnetic waves
    10. 10.10. Electromagnetic spectrum
    11. 10.11. Emission of electromagnetic radiations
    12. 10.12. Spontaneous and stimulated emissions
    13. 10.13. Problems
  17. Chapter 11. Reflection, Interference, Diffraction and Diffusion
    1. 11.1. General laws of reflection and refraction
    2. 11.2. Reflection and refraction on the interface of two dielectrics
    3. 11.3. Total reflection
    4. 11.4. Reflection on a conductor
    5. 11.5. Reflection on a plasma
    6. 11.6. Interference of two electromagnetic waves
    7. 11.7. Superposition of several waves, conditions for observable interference
    8. 11.8. Huygens-Fresnel’s principle and diffraction by an aperture
    9. 11.9. Diffraction by an obstacle, Babinet’s theorem
    10. 11.10. Diffraction by several randomly distributed identical apertures
    11. 11.11. Diffraction grating
    12. 11.12. X-ray diffraction
    13. 11.13. Diffusion of waves*
    14. 11.14. Cross-section*
    15. 11.15. Problems
  18. Chapter 12. Guided Waves
    1. 12.1. Transmission lines
    2. 12.2. Guided waves
    3. 12.3. Waveguides formed by two plane and parallel plates
    4. 12.4. Guided electromagnetic waves in a hollow conductor
    5. 12.5. Energy propagation in waveguides
    6. 12.6. Cavities
    7. 12.7. Applications of waveguides
    8. 12.8. Problems
  19. Chapter 13. Special Relativity and Electrodynamics
    1. 13.1. Galilean relativity in mechanics
    2. 13.2. Galilean relativity and wave theory*
    3. 13.3. The 19th Century experiments on the velocity of light
    4. 13.4. Special theory of relativity
    5. 13.5. Four-dimensional formalism
    6. 13.6. Elements of relativistic mechanics
    7. 13.7. Special relativity and wave theory*
    8. 13.8. Elements of relativistic electrodynamics
    9. 13.9. Problems
  20. Chapter 14. Motion of Charged Particles in an Electromagnetic Field
    1. 14.1. Motion of a charged particle in an electric field
    2. 14.2. Bohr model for the hydrogen atom*
    3. 14.3. Rutherford’s scattering *
    4. 14.4. Motion of a charged particle in a magnetic field
    5. 14.5. Motion in crossed electric and magnetic fields
    6. 14.6. Magnetic moment in a magnetic field
    7. 14.7. Problems
  21. Chapter 15. Emission of Radiation
    1. 15.1. Retarded potentials and fields
    2. 15.2. Dipole radiation
    3. 15.3. Electric dipole radiation
    4. 15.4. Magnetic dipole radiation
    5. 15.5. Antennas
    6. 15.6. Potentials and fields of a charged particle*
    7. 15.7. Case of a charged particle with constant velocity *
    8. 15.8. Radiated energy by a moving charge
    9. 15.9. Problems
  22. Answers to Some Problems
  23. Appendix A. Mathematical Review
  24. Appendix B. Units in Physics
  25. Appendix C. Some Physical Constants
  26. Further Reading
  27. Index