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
- Coverpage
- Titlepage
- Copyright
- Table of Contents
- Preface
- List of Symbols
-
Chapter 1. Prologue
- 1.1. Scalars and vectors
- 1.2. Effect of rotations on scalars and vectors
- 1.3. Integrals involving vectors
- 1.4. Gradient and curl, conservative field and scalar potential
- 1.5. Divergence, conservative flux, and vector potential
- 1.6. Other properties of the vector differential operator
- 1.7. Invariance and physical laws
- 1.8. Electric charges in nature
- 1.9. Interactions in nature
- 1.10. Problems
-
Chapter 2. Electrostatics in Vacuum
- 2.1. Electric forces and field
- 2.2. Electric energy and potential
- 2.3. The two fundamental laws of electrostatics
- 2.4. Poisson’s equation and its solutions
- 2.5. Symmetries of the electric field and potential
- 2.6. Electric dipole
- 2.7. Electric field and potential of simple charge configurations
- 2.8. Some general properties of the electric field and potential
- 2.9. Electrostatic energy of a system of charges
- 2.10. Electrostatic binding energy of ionic crystals and atomic nuclei
- 2.11. Interaction-at-a-distance and local interaction*
- 2.12. Problems
-
Chapter 3. Conductors and Currents
- 3.1. Conductors in equilibrium
- 3.2. Conductors with cavities, electric shielding
- 3.3. Capacitors
- 3.4. Mutual electric influence of conductors
- 3.5. Electric forces between conductors
- 3.6. Currents and current densities
- 3.7. Classical model of conduction, Ohm’s law and the Joule effect
- 3.8. Resistance of conductors
- 3.9. Variation of resistivity with temperature, superconductivity
- 3.10. Band theory of conduction, semiconductors*
- 3.11. Electric circuits
- 3.12. Problems
-
Chapter 4. Dielectrics
- 4.1. Effects of dielectric on capacitors
- 4.2. Polarization of dielectrics
- 4.3. Microscopic interpretation of polarization
- 4.4. Polarization charges in dielectric
- 4.5. Potential and field of polarized dielectrics
- 4.6. Gauss’s law in the case of dielectrics, electric displacement
- 4.7. Electrostatic equations in dielectrics
- 4.8. Field and potential of permanent dielectrics
- 4.9. Polarization of a dielectric in an external field
- 4.10. Energy and force in dielectrics
- 4.11. Action of an electric field on a polarized medium
- 4.12. Electric susceptibility and permittivity
- 4.13. Variation of polarization with temperature
- 4.14. Nonlinear dielectrics and non-isotropic dielectrics
- 4.15. Problems
-
Chapter 5. Special Techniques and Approximation Methods
- 5.1. Unicity of the solution
- 5.2. Method of images
- 5.3. Method of analytic functions
- 5.4. Method of separation of variables
- 5.5. Laplace’s equation in Cartesian coordinates
- 5.6. Laplace’s equation in spherical coordinates
- 5.7. Laplace’s equation in cylindrical coordinates
- 5.8. Multipole expansion
- 5.9. Other methods
- 5.10. Problems
-
Chapter 6. Magnetic Field in Vacuum
- 6.1. Force exerted by a magnetic field on a moving charge
- 6.2. Force exerted by a magnetic field on a current, Laplace’s force
- 6.3. Magnetic flux and vector potential
- 6.4. Magnetic field of particles and currents, Biot-Savart’s law
- 6.5. Magnetic moment
- 6.6. Symmetries of the magnetic field
- 6.7. Ampère’s law in the integral form
- 6.8. Field and potential of some simple circuits
- 6.9. Equations of time-independent magnetism in vacuum, singularities of B
- 6.10. Magnetic energy of a circuit in a field B
- 6.11. Magnetic forces
- 6.12. Question of magnetic monopoles*
- 6.13. Problems.
-
Chapter 7. Magnetism in Matter
- 7.1. Types of magnetism
- 7.2. Diamagnetism and paramagnetism
- 7.3. Magnetization current
- 7.4. Magnetic field and vector potential in the presence of magnetic matter
- 7.5. Ampère’s law in the integral form in the presence of magnetic matter
- 7.6. Equations of time-independent magnetism in the presence of matter
- 7.7. Discontinuities of the magnetic field
- 7. 8. Examples of calculation of the field of permanent magnets
- 7.9. Magnetization of a body in an external field
- 7.10. Magnetic susceptibility, nonlinear mediums and non-isotropic mediums
- 7.11. Action of a magnetic field on a magnetic body
- 7.12. Magnetic energy in matter
- 7.13. Variation of magnetization with temperature
- 7.14. Ferromagnetism
- 7.15. Magnetic circuits
- 7.16. Problems
-
Chapter 8. Induction
- 8.1. Induction due to the variation of the flux, Faraday’s and Lenz’s laws
- 8.2. Neumann’s induction
- 8.3. Lorentz induction
- 8.4. Lorentz induction and the Galilean transformation of fields
- 8.5. Mutual inductance and self-inductance
- 8.6. LR circuit
- 8.7. Magnetic energy
- 8.8. Magnetic forces acting on circuits
- 8.9. Some applications of induction
- 8.10. Problems
-
Chapter 9. Maxwell’s Equations
- 9.1. Fundamental laws of electromagnetism
- 9.2. Maxwell’s equations
- 9.3. Electromagnetic potentials and gauge transformation
- 9.4. Quasi-permanent approximation
- 9.5. Discontinuities on the interface of two mediums
- 9.6. Electromagnetic energy and Poynting vector
- 9.7. Electromagnetic pressure, Maxwell’s tensor
- 9.8. Problems
-
Chapter 10. Electromagnetic Waves
- 10.1. A short review on waves
- 10.2. Electromagnetic waves in infinite vacuum and dielectrics
- 10.3. Polarization of electromagnetic waves
- 10.4. Energy and intensity of plane electromagnetic waves
- 10.5. Momentum and angular momentum densities, radiation pressure
- 10.6. A simple model of dispersion
- 10.7. Electromagnetic waves in conductors
- 10.8. Electromagnetic waves in plasmas
- 10.9. Quantization of electromagnetic waves
- 10.10. Electromagnetic spectrum
- 10.11. Emission of electromagnetic radiations
- 10.12. Spontaneous and stimulated emissions
- 10.13. Problems
-
Chapter 11. Reflection, Interference, Diffraction and Diffusion
- 11.1. General laws of reflection and refraction
- 11.2. Reflection and refraction on the interface of two dielectrics
- 11.3. Total reflection
- 11.4. Reflection on a conductor
- 11.5. Reflection on a plasma
- 11.6. Interference of two electromagnetic waves
- 11.7. Superposition of several waves, conditions for observable interference
- 11.8. Huygens-Fresnel’s principle and diffraction by an aperture
- 11.9. Diffraction by an obstacle, Babinet’s theorem
- 11.10. Diffraction by several randomly distributed identical apertures
- 11.11. Diffraction grating
- 11.12. X-ray diffraction
- 11.13. Diffusion of waves*
- 11.14. Cross-section*
- 11.15. Problems
- Chapter 12. Guided Waves
-
Chapter 13. Special Relativity and Electrodynamics
- 13.1. Galilean relativity in mechanics
- 13.2. Galilean relativity and wave theory*
- 13.3. The 19th Century experiments on the velocity of light
- 13.4. Special theory of relativity
- 13.5. Four-dimensional formalism
- 13.6. Elements of relativistic mechanics
- 13.7. Special relativity and wave theory*
- 13.8. Elements of relativistic electrodynamics
- 13.9. Problems
- Chapter 14. Motion of Charged Particles in an Electromagnetic Field
-
Chapter 15. Emission of Radiation
- 15.1. Retarded potentials and fields
- 15.2. Dipole radiation
- 15.3. Electric dipole radiation
- 15.4. Magnetic dipole radiation
- 15.5. Antennas
- 15.6. Potentials and fields of a charged particle*
- 15.7. Case of a charged particle with constant velocity *
- 15.8. Radiated energy by a moving charge
- 15.9. Problems
- Answers to Some Problems
- Appendix A. Mathematical Review
- Appendix B. Units in Physics
- Appendix C. Some Physical Constants
- Further Reading
- Index
Product information
- Title: Electromagnetism: Maxwell Equations, Wave Propagation and Emission
- Author(s):
- Release date: July 2012
- Publisher(s): Wiley-ISTE
- ISBN: 9781848213555
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