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 Cud of a Vector Function
2.2.4 Del Identities
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 Cud 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
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