1 History and Perspective

1.1 Brief History of the Science of Electromagnetism

1.2 Electromagnetism in the Standard Model

2 Vector Calculus

2.1 Vector Algebra

2.1.1 Definitions

2.1.2 Addition and Multiplication of Vectors

2.1.3 Vector Product Identities

2.1.4 Geometric Meanings

2.2 Vector Differential Operators

2.2.1 Gradient of a Scalar Function

2.2.2 Divergence of a Vector Function

2.2.3 Curl of a Vector Function

2.2.4 DelIdentities

2.3 Integral Theorems

2.3.1 Gauss’s Theorem

2.3.2 Stokes’s Theorem

2.3.3 Vector Calculus in Fluid Mechanics

2.4 Curvilinear Coordinates

2.4.1 General Derivations

2.4.2 Cartesian, Cylindrical, and Spherical Coordinates

2.5 The Helmholtz Theorem

3 Basic Principles of Electrostatics

3.1 Coulomb’s Law

3.1.1 The Superposition Principle

3.2 The Electric Field

3.2.1 Definition

3.2.2 Charge as the Source of E

3.2.3 Field of a Charge Continuum

3.3 Curl and Divergence of E

3.3.1 Field Theory Versus Action at a Distance

3.3.2 Boundary Conditions of the Electrostatic Field

3.4 The Integral Form of Gauss’s Law

3.4.1 Flux and Charge

3.4.2 Proof of Gauss’s Law

3.4.3 Calculations Based on Gauss’s Law

3.5 Green’s Function and the Dirac delta Function

3.5.1 The Dirac delta Function

3.5.2 Another Proof of Gauss’s Law

3.6 The Electric Potential

3.6.1 Definition and Construction

3.6.2 Poisson’s Equation

3.6.3 Example Calculations of V （x）

3.7 Energy of the Electric Field

3.8 The Multipole Expansion

3.8.1 Two Charges

3.8.2 The Electric Dipole

3.8.3 Moments of a General Charge Distribution

3.8.4 Equipotentials and Field Lines

3.8.5 Torque and Potential Energy for a Dipole in an Electric Field

3.9 Applications

3.10 Chapter Summary

4 Electrostatics and Conductors

4.1 Electrostatic properties of conductors

4.2 Electrostatic Problems with Rectangular Symmetry

4.2.1 Charged Plates

4.2.2 Problems with Rectangular Symmetry and External Point Charges.The Method of Images

4.3 Problems with Spherical Symmetry

4.3.1 Charged Spheres

4.3.2 Problems with Spherical Symmetry and External Charges

4.4 Problems with Cylindrical Symmetry

4.4.1 Charged Lines and Cylinders

4.4.2 Problems with Cylindrical Symmetry and an External Line Charge

5 General Methods for Laplace’s Equation

5.1 Separation of Variables for Cartesian Coordinates

5.1.1 Separable Solutions for Cartesian Coordinates

5.1.2 Examples

5.2 Separation of Variables for Spherical Polar Coordinates

5.2.1 Separable Solutions for Spherical Coordinates

5.2.2 Legendre Polynomials

5.2.3 Examples with Spherical Boundaries

5.3 Separation of Variables for Cylindrical Coordinates

5.3.1 Separable Solutions for Cylindrical Coordinates

5.4 Conjugate Functions in 2 Dimensions

5.5 Iterative Relaxation: A Numerical Method

6 Electrostatics and Dielectrics

6.1 The Atom as an Electric Dipole

6.1.1 Induced Dipoles

6.1.2 Polar Molecules

6.2 Polarization and Bound Charge

6.3 The Displacement Field

6.3.1 Linear Dielectrics

6.3.2 The Clausius-Mossotti Formula

6.3.3 Poisson’s Equation in a Uniform Linear Dielectric

6.4 Dielectric Material in a Capacitor

6.4.1 Design of Capacitors

6.4.2 Microscopic Theory

6.4.3 Energy in a Capacitor

6.4.4 A Concrete Model of a Dielectric

6.5 Boundary Value Problems with Dielectrics

6.5.1 The Boundary Conditions

6.5.2 A Dielectric Sphere in an Applied Field

6.5.3 A Point Charge above a Dielectric with a Planar Bound-ary Surface

6.5.4 A Capacitor Partially Filled with Dielectric

7 Electric Currents

7.1 Electric Current in a Wire

7.2 Current Density and the Continuity Equation

7.2.1 Local Conservation of Charge

7.2.2 Boundary Condition on J（x, t）

7.3 Current and Resistance

7.3.1 Ohm’s Law

7.3.2 Fabrication of Resistors

7.3.3 The Surface Charge on a Current Carrying Wire

7.4 A Classical Model of Conductivity

7.5 Joule’s Law

7.6 Decay of a Charge Density Fluctuation

7.7 Ⅰ-Ⅴ Characteristic of a Vacuum-Tube Diode

7.8 Chapter Summary

8 Magnetostatics

8.1 The Magnetic Force and the Magnetic Field

8.1.1 Force on a Moving Charge

8.1.2 Force on a Current-Carrying Wire

8.2 Applications of the Magnetic Force

8.2.1 Helical or Circular Motion of q in Uniform B

8.2.2 Cycloidal Motion of q in Crossed E and B

8.2.3 Electric Motors

8.3 Electric Current as a Source of Magnetic Field

8.3.1 The Biot-Savart Law

8.3.2 Forces on Parallel Wires

8.3.3 General Field Equations for B（x）

8.4 Ampere’s Law

8.4.1 Ampere Law Calculations

8.4.2 Formal Proof of Ampere’s Law

8.5 The Vector Potential

8.5.1 General Solution for A（x）

8.6 The Magnetic Dipole

8.6.1 Asymptotic Analysis

8.6.2 Dipole Moment of a Planar Loop

8.6.3 Torque and Potential Energy of a Magnetic Dipole

8.6.4 The Magnetic Field of the Earth

8.7 The Full Field of a Current Loop

9 Magnetic Fields and Matter

9.1 The Atom as a Magnetic Dipole

9.1.1 Diamagnetism

9.1.2 Paramagnetism

9.2 Magnetization and Bound Currents

9.2.1 Examples

9.2.2 A Geometric Derivation of the Bound Currents

9.3 Ampere’s Law for Free Currents, and H

9.3.1 The Integral Form of Ampere’s Law

9.3.2 The Constitutive Equation

9.3.3 Magnetic Susceptibilities

9.3.4 Boundary Conditions for Magnetic Fields

9.4 Problems Involving Free Currents and Magnetic Materials

9.5 A Magnetic Body in an External Field: The Magnetic Scalar Potentialφm （x）

9.6 Ferromagnetism

9.6.1 Measuring Magnetization Curves: The Rowland Ring

9.6.2 Magnetization Curves of Ferromagnetic Materials

9.6.3 The Permeability of a Ferromagnetic Material

10 Electromagnetic Induction

10.1 Motional EMF

10.1.1 Electromotive Force

10.1.2 EMF from Motion in B

10.1.3 The Faraday Disk Generator

10.2 Faraday’s Law of Electromagnetic Induction

10.2.1 Mathematical Statement

10.2.2 Lenz’s Law

10.2.3 Eddy Currents

10.3 Applications of Faraday’s Law

10.3.1 The Electric Generator and Induction Motor

10.3.2 The Betatron

10.3.3 Self-Inductance

10.3.4 Classical Model of Diamagnetism

10.4 Mutual Inductance

10.5 Magnetic Field Energy

10.5.1 Energy in a Ferromagnet

11 The Maxwell Equations

11.1 The Maxwell Equations in Vacuum and the Displacement Current

11.1.1 The Displacement Current

11.2 Scalar and Vector Potentials

11.2.1 Gauge Transformations and Gauge Invariance

11.2.2 Gauge Choices and Equations for A（x,t） and V（x,t）

11.3 The Maxwell Equations in Matter

11.3.1 Free and Bound Charge and Current

11.3.2 Boundary Conditions of Fields

11.4 Energy and Momentum of Electromagnetic Fields

11.4.1 Poynting’s Theorem

11.4.2 Field Momentum

11.5 Electromagnetic Waves in Vacuum

11.5.1 Derivation of the Wave Equation

11.5.2 An Example of a Plane Wave Solution

11.5.3 Derivation of the General Plane Wave Solution

11.5.4 A Spherical Harmonic Wave

11.5.5 The Theory of Light

12 Electromagnetism and Relativity

12.1 Coordinate Transformations

12.1.1 The Galilean Transformation

12.1.2 The Lorentz Transformation

12.1.3 Examples Involving the Lorentz Transformation

12.2 Minkowski Space

12.2.1 4-vectors, Scalars, and Tensors

12.2.2 Kinematics of a Point Particle

12.2.3 Relativistic Dynamics

12.3 Electromagnetism in Covariant Form

12.3.1 The Lorentz Force and the Field Tensor

12.3.2 Maxwell’s Equations in Covariant Form

12.3.3 The 4-vector Potential

12.4 Field Transformations

12.5 Fields Due to a Point Charge in Uniform Motion

12.6 Magnetism from Relativity

12.7 The Energy-Momentum Flux Tensor

13 Electromagnetism and Optics

13.1 Electromagnetic Waves in a Dielectric

13.2 Reflection and Refraction at a Dielectric Interface

13.2.1 Wave Vectors

13.2.2 Reflectivity for Normal Incidence

13.2.3 Reflection for Incidence at Arbitrary Angles: Fresnel’s Equations

13.3 Electromagnetic Waves in a Conductor

13.3.1 Reflectivity of a Good Conductor

13.4 A Classical Model of Dispersion: The Frequency Dependence of Material Properties

13.4.1 Dispersion in a Dielectric

13.4.2 Dispersion in a Plasma

14 Wave Guides and Transmission Lines

14.1 Electromagnetic Waves Between Parallel Conducting Planes

14.1.1 The TEM Solution

14.1.2 TE Waves

14.1.3 TM Waves

14.1.4 Summary

14.2 The Rectangular Wave Guide

14.2.1 Transverse Electric Modes TE（m, n）

14.2.2 Transverse Magnetic Modes TM（m, n）

14.3 Wave Guide of Arbitrary Shape

14.4 The TEM Mode of a Coaxial Cable

14.5 Cavity Resonance

15 Radiation of Electromagnetic Waves

15.1 The Retarded Potentials

15.1.1 Green’s Functions

15.2 Radiation from an Electric Dipole

15.2.1 The Hertzian Dipole

15.2.2 Atomic Transitions

15.2.3 Magnetic Dipole Radiation

15.2.4 Complete Fields of a Hertzian Dipole

15.3 The Half-Wave Linear Antenna

15.4 The Larmor Formula: Radiation from a Point Charge

15.5 Classical Electron Theory of Light Scattering

15.6 Complete Fields of a Point Charge: The Lienard-Wiechert Potentials

15.6.1 A Charge with Constant Velocity

15.6.2 The Complete Fields

15.6.3 Generalization of the Larmor Formula

A Electric and Magnetic Units

B The Helmholtz Theorem

Index