Maxwell's Equations

Introduction.

1 Foundations of Maxwell’s Equations.

1.1 Historical Overview.

1.2 Role of Electromagnetic Field Theory.

1.3 Electromagnetic Field Quantities.

1.4 Units and Universal Constants.

1.5 Precision of Measured Quantities.

1.6 Introduction to Complex Variables.

1.7 Phasor Notation.

1.8 Quaternions.

1.9 Original Form of Maxell’s Equations.

2 Vector Analysis.

Introduction.

2.1 Addition and Subtraction.

2.2 Multiplication.

2.3 Triple Products.

2.4 Coordinate Systems.

2.5 Coordinate Transformations.

2.6 Vector Differentiation.

2.7 Divergence Theorem.

2.8 Stokes's Theorem.

2.9 Laplacian of a Vector Field.

3 Static Electric Fields.

Introduction.

3.1 Properties of Electrostatic Fields.

3.2 Gauss’s Law.

3.3 Conservation Law.

3.4 Electric Potential.

3.5 Electric Field for a System of Charges.

3.6 Electric Potential for a System of Charges.

3.7 Electric Field for a Continuous Distribution.

3.8 Conductor in a Static Electric Field.

3.9 Capacitance.

3.10 Dielectrics.

3.11 Electric Flux Density.

3.12 Dielectric Boundary Conditions.

3.13 Electrostatic Energy.

3.14 Electrostatic Field in a Dielectric.

Endnotes.

4 Solution of Electrostatic Problems.

Introduction.

4.1 Poisson’s and Laplace’s Equations.

4.2 Solutions to Poisson’s and Laplace’s Equations.

4.3 Green’s Functions.

4.4 Uniqueness of the Electrostatic Solution.

4.5 Method of Images.

5 Steady Electric Currents.

5.1 Current Density and Ohm’s Law.

5.2 Relation to Circuit Parameters.

5.3 Superconductivity.

5.4 Free Electron Gas Theory.

5.5 Band Theory.

5.6 Equation of Continuity.

5.7 Microscopic View of Ohm’s Law.

5.8 Power Dissipation and Joule’s Law.

5.9 Boundary Condition for Current Density.

5.10 Resistance/Capacitance Calculations.

Endnotes.

6 Static Magnetic Fields.

Introduction.

6.1 Magnetic Force.

6.2 Magnetostatics in Free Space.

6.3 Magnetic Vector Potential.

6.4 The Biot-Savart Law.

6.5 Historical Conclusions.

6.6 Atomic Magnetism.

6.7 Magnetization.

6.8 Equivalent Surface Current Density.

6.9 Equivalent Magnetic Monopole Charge Density.

6.10 Magnetic Field Intensity and Permeability.

6.11 Ferromagnetism.

6.12 Boundary Conditions for Magnetic Fields.

6.13 Inductance and Inductors.

6.14 Torque and Energy.

Endnotes.

7 Time-Varrying Fields.

7.1 Faraday’s Law of Induction.

7.2 E&M Equations before Maxwell.

7.3 Maxwell’s Displacement Current.

7.4 Integral Form of Maxwell’s Equations.

7.5 Magnetic Vector Potential.

7.6 Solution of the Time-Dependent Inhomogeneous Potential Wave Equations.

7.7 Electric and Magnetic Field Equations for Source-Free Problems.

7.8 Solutions for the Homogeneous Wave Equation.

7.9 Particular Solution for the Inhomogeneous Wave Equation.

7.10 Time Harmonic Fields.

7.11 Electromagnetic Spectrum.

7.12 Electromagnetic Boundary Conditions.

7.13 Particular Solution for the Wave Equation with Inhomogeneous Boundary Conditions.

7.14 Memristors.

7.15 Electric Vector Potential.

APPENDIX A: MEASUREMENT ERRORS.

APPENDIX B: GRAPHICS AND CONFORMAL MAPPING.

APPENDIX C: VECTORS, MATRICEES, ORTHOGONAL FUNCTIONS.

BIBLIOGRAPHY.

Index.