Maxwell's Equations and the Principles of Electromagnetism

Author:            Richard Fitzpatrick

Publisher:         Jones and Bartlett Learning

Publication Date:  2008

ISBN:              978-1-934015-20-9

Designed for upper division electromagnetism courses or as reference for electrical engineers and scientists, this book introduces Maxwell's equations and electromagnetic waves as soon as possible (i.e., in the first third of the book), and then discusses electrostatics, magnetostatics, induction, etc., in the light of those equations. The book also provides a thourough treatment of vector field theory which emphasizes the rotational invariance of the dot and cross products, together with div, grad, and curl, and thus gives a clear physical motivation for the use of these constructs to describe electric and magnetic fields. Unlike many competing books, Maxwell's Equations and the Principles of Electromagnetism covers topics such as advanced potentials, retarded fields, forces on dielectric liquids, antenna theory, and Faraday rotation.

1. Introduction.

2. Vectors and Vector Fields. Introduction; Vector Algebra; Vector Areas; The Scalar Product; The Vector Product; Rotation; The Scalar Triple Product; The Vector Triple Product; Vector Calculus; Line Integrals; Vector Line Integrals; Surface Integrals; Vector Surface Integrals; Volume Integrals; Gradient; Divergence; The Laplacians; Curl; Polar Coordinates; Exercises.

3. Time-Independent Maxwell Equations. Introduction; Coulomb's Law; The Electric Scalar Potential; Gauss' Law; Poisson's Equation; Ampere's Experiments; The Lorentz Force; Ampere's Law; Magnetic Monopoles? Ampere's Circuital Law; Helmholtz's Theorem; The Magnetic Vector Potential; The Biot-Savart Law; Electrostatics and Magnetostatics; Exercises.

4. Time-Dependent Maxwell Equations. Introduction; Faraday's Law; Electric Scalar Potential? Gauge Transformations; The Displacement Current; Potential Formulation; Electromagnetic Waves; Green's Functions; Retarded Potentials; Advanced Potentials? Retarded Fields; Maxwell's Equations; Exercises.

5. Electrostatic Calculations. Introduction; Electrostatic Energy; Ohm's Law; Conductors; Boundary Conditions on the Electric Field; Capacitors; Poisson's Equation; The Uniqueness Theorem; One-Dimensional Solutions of Poisson's Equation; The Method of Images; Complex Analysis; Separation of Variables; Exercises.

6. Dielectric and Magnetic Media. Introduction; Polarization; Electric Susceptability and Permittivity; Boundary Conditons for E and D; Boundary Value Problems with Dielectrics; Energy Density within a Dielectic Medium; Force Density within a Dielectic Medium; The Clausius-Mossotti Relation; Dielectic Liquids in Electrostatic Fields; Polarization Current; Magnetization; Magnetic Susceptibility and Permeability; Ferromagnetism; Boundary Conditions for B and H; Boundary Value Problems with Ferromagnets; Magnetic Energy; Exercises.

7. Magnetic Induction. Introduction; Inductance; Self-Inductance; Mutual Inductance; Magnetic Energy; Alternating Current Circuits; Transmission Lines; Exercises.

8. Electromagnetic Energy and Momentum. Introduction; Energy Conservation; Electromagnetic Momentum; Momentum Conservation; Angular Momentum Conservation; Exercises.

9. Electromagnetic Radiation. Introduction; The Hertzian Dipole; Electric Dipole Radiation; Thompson Scattering; Rayleigh Scattering; Propagation in a Dielectric Medium; Dielectric Constant of a Gaseous Medium; Dispersion Relation of a Plasma; Faraday Rotation; Propagation in a Conductor; Dispersion Relation of a Collisional Plasma; Normal Reflection at a Dielectric Boundary; Oblique Reflection at a Dielectric Boundary; Total Internal Reflection; Optical Coatings; Reflection at a Metallic Boundary; Wave-Guides; Exercises.

10. Relativity and Electromagnetism. Introduction; The Relativity Principle; The Lorentz Transformation; Transformation of Velocities; Tensors; Physical Significance of Tensors; Space-Time; Proper Time; 4-Velocity and 4-Acceleration; The Current Density 4-Vector; The Potential 4-Vector; Gauge Invariance; Retarded Potentials; Tensors and Pseudo-Tensors; The Electromagnetic Field Tensor; The Dual Electromagnetic Field Tensor; Transformation of Fields; Potential Due to a Moving Charge; Relativistic Particle Dynamics; Force on a Moving Charge; The Electromagnetic Energy Tensor; Accelerated Charges; The Larmor Formula; Radiation Losses; Angular Distribution of Radiation; Syncrotron Radiation; Exercises.

A. Physical Constants.

B. Useful Vector Identities.

C. Gaussian Units.

C. Further Reading.