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Maxwell's Equations
Classical Electromagnetism
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Maxwell's Equations
Introduction
Maxwell's Equations
Scalar and Vector Potentials
Dirac Delta Function
Three-Dimensional Dirac Delta Function
Solution of Inhomogeneous Wave Equation
Retarded Potentials
Retarded Fields
Electromagnetic Energy Conservation
Electromagnetic Momentum Conservation
Exercises
Electrostatic Fields
Introduction
Laplace's Equation
Poisson's Equation
Coulomb's Law
Electric Scalar Potential
Electrostatic Energy
Electric Dipoles
Charge Sheets and Dipole Sheets
Green's Theorem
Boundary Value Problems
Dirichlet Green's Function for Spherical Surface
Exercises
Potential Theory
Introduction
Associated Legendre Functions
Spherical Harmonics
Laplace's Equation in Spherical Coordinates
Poisson's Equation in Spherical Coordinates
Multipole Expansion
Axisymmetric Charge Distributions
Dirichlet Problem in Spherical Coordinates
Newmann Problem in Spherical Coordinates
Laplace's Equation in Cylindrical Coordinates
Poisson's Equation in Cylindrical Coordinates
Exercises
Electrostatics in Dielectric Media
Polarization
Boundary Conditions for
and
Boundary Value Problems with Dielectrics
Energy Density Within Dielectric Medium
Force Density Within Dielectric Medium
Clausius-Mossotti Relation
Dielectric Liquids in Electrostatic Fields
Exercises
Magnetostatic Fields
Introduction
Biot-Savart Law
Continuous Current Distribution
Circular Current Loop
Localized Current Distribution
Exercises
Magnetostatics in Magnetic Media
Magnetization
Magnetic Susceptibility and Permeability
Ferromagnetism
Boundary Conditions for
and
Permanent Ferromagnets
Uniformly Magnetized Sphere
Soft Iron Sphere in Uniform Magnetic Field
Magnetic Shielding
Magnetic Energy
Exercises
Wave Propagation in Uniform Dielectric Media
Introduction
Form of Dielectric Constant
Anomalous Dispersion and Resonant Absorption
Wave Propagation in Conducting Media
High Frequency Limit
Polarization of Electromagnetic Waves
Faraday Rotation
Wave Propagation in Magnetized Plasmas
Wave Propagation in Dispersive Media
Wave-Front Propagation
Sommerfeld Precursor
Method of Stationary Phase
Group Velocity
Brillouin Precursor
Signal Arrival
Exercises
Wave Propagation in Inhomogeneous Dielectric Media
Introduction
Laws of Geometric Optics
Fresnel Relations
Total Internal Reflection
Reflection by Conducting Surfaces
Ionospheric Radio Wave Propagation
WKB Approximation
Reflection Coefficient
Extension to Oblique Incidence
Ionospheric Pulse Propagation
Measurement of Ionospheric Electron Density Profile
Ionospheric Ray Tracing
Asymptotic Series
WKB Solution as Asymptotic Series
Stokes Constants
WKB Reflection Coefficient
Jeffries Connection Formula
Exercises
Radiation and Scattering
Introduction
Basic Antenna Theory
Antenna Directivity and Effective Area
Antenna Arrays
Thomson Scattering
Rayleigh Scattering
Exercises
Resonant Cavities and Waveguides
Introduction
Boundary Conditions
Cavities with Rectangular Boundaries
Quality Factor of a Resonant Cavity
Axially Symmetric Cavities
Cylindrical Cavities
Waveguides
Dielectric Waveguides
Exercises
Multipole Expansion
Introduction
Multipole Expansion of Scalar Wave Equation
Angular Momentum Operators
Multipole Expansion of Vector Wave Equation
Properties of Multipole Fields
Solution of Inhomogeneous Helmholtz Equation
Sources of Multipole Radiation
Radiation from Linear Centre-Fed Antenna
Spherical Wave Expansion of Vector Plane Wave
Mie Scattering
Exercises
Relativity and Electromagnetism
Introduction
Relativity Principle
Lorentz Transformation
Transformation of Velocities
Tensors
Physical Significance of Tensors
Space-Time
Proper Time
4-Velocity and 4-Acceleration
Current Density 4-Vector
Potential 4-Vector
Gauge Invariance
Retarded Potentials
Tensors and Pseudo-Tensors
Electromagnetic Field Tensor
Dual Electromagnetic Field Tensor
Transformation of Fields
Potential Due to a Moving Charge
Field Due to a Moving Charge
Relativistic Particle Dynamics
Force on a Moving Charge
Electromagnetic Energy Tensor
Accelerated Charges
Larmor Formula
Radiation Losses
Angular Distribution of Radiation
Synchrotron Radiation
Exercises
About this document ...
Richard Fitzpatrick 2014-06-27
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