Maxwell’s Integral Laws in Free Space

•  1.0 Introduction

-Overview of Subject

 

•  1.1 The Lorentz Law in Free Space

•  1.2 Charge and Current Densities

•  1.3 Gauss’ Integral Law of Electric Field Intensity

-Singular Charge Distributions

-Gauss’ Continuity Condition

 

•  1.4 Ampère’s Integral Law

-Singular Current Distributions

-Ampère’s Continuity Conditions

 

•  1.5 Charge Conservation in Integral Form

-Charge Conservation Continuity Condition

 

•  1.6 Faraday’s Integral Law

-Electric Field Intensity Having No Circulation

-Electric Field Intensity With Circulation

-Faraday’s Continuity Condition

 

•  1.7 Gauss’ Integral Law of Magnetic Flux

-Magnetic Flux Continuity Condition

 

Maxwell’s Differential Laws In Free Space

•  2.0 Introduction

•  2.1 The Divergence Operator

•  2.2 Gauss’ Integral Theorem

•  2.3 Gauss’ Law, Magnetic Flux Continuity, and ChargeConservation

•  2.4 The Curl Operator

•  2.5 Stokes’ Integral Theorem

•  2.6 Differential Laws of Ampère and Faraday

•  2.7 Visualization of Fields and the Divergence and Curl

•  2.8 Summary of Maxwell’s Differential Laws and Integral Theorems

Introduction To Electroquasistatics and Magnetoquasistatics

•  3.0 Introduction

•  3.1 Temporal Evolution of World Governed by Laws ofMaxwell, Lorentz, and Newton

•  3.2 Quasistatic Laws

•  3.3 Conditions for Fields to be Quasistatic

•  3.4 Quasistatic Systems1

•  3.5 Overview of Applications

•  3.6 Summary

 

Electroquasistatic Fields: The Superposition Integral Point of View

•  4.0 Introduction

•  4.1 Irrotational Field Represented by Scalar Potential: TheGradient Operator and Gradient Integral Theorem

•  4.2 Poisson’s Equation

•  4.3 Superposition Principle

•  4.4 Fields Associated with Charge Singularities

•  4.5 Solution of Poisson’s Equation for Specified ChargeDistributions

•  4.6 Electroquasistatic Fields in the Presence of PerfectConductors

•  4.7 Method of Images

•  4.8 Charge Simulation Approach to Boundary Value Problems

•  4.9 Summary

 

Electroquasistatic Fields from the Boundary Value Point of View

•  5.1 Particular and Homogeneous Solutions to Poisson’sand Laplace’s Equations

•  5.2 Uniqueness of Solutions to Poisson’s Equation

•  5.3 Continuity Conditions

•  5.4 Solutions to Laplace’s Equation in CartesianCoordinates

•  5.5 Modal Expansion to Satisfy Boundary Conditions

•  5.6 Solutions to Poisson’s Equation with BoundaryConditions

•  5.7 Solutions to Laplace’s Equation in Polar Coordinates

•  5.8 Examples in Polar Coordinates

•  5.9 Three Solutions to Laplace’s Equation inSpherical Coordinates

•  5.10 Three-Dimensional Solutions to Laplace’s Equation

 

Polarization

•  6.1 Polarization Density

•  6.2 Laws and Continuity Conditions with Polarization

•  6.3 Permanent Polarization

•  6.4 Constitutive Laws of Polarization

•  6.5 Fields in the Presence of Electrically LinearDielectrics

•  6.6 Piece-Wise Uniform Electrically Linear Dielectrics

•  6.7 Smoothly Inhomogeneous Electrically LinearDielectrics

 

Conduction and Electroquasistatic Charge Relaxation

•  7.1 Conduction Constitutive Laws

•  7.2 Steady Ohmic Conduction

•  7.3 Distributed Current Sources and Associated Fields

•  7.4 Superposition and Uniqueness of Steady Conduction Solutions

•  7.5 Steady Currents in Piece-Wise Uniform Conductors

•  7.6 Conduction Analogs

•  7.7 Charge Relaxation in Uniform Conductors

•  7.8 Electroquasistatic Conduction Laws forInhomogeneous Materials

•  7.9 Charge Relaxation in Uniform and Piece-Wise UniformSystems

 

Magnetoquasistatic Fields: Superposition Integral and Boundary Value Points of View

•  8.1 The Vector Potential and the Vector Poisson Equation

•  8.2 The Biot-Savart Superposition Integral

•  8.3 The Scalar Magnetic Potential

•  8.4 Magnetoquasistatic Fields in the Presence of PerfectConductors

•  8.5 Piece-Wise Magnetic Fields

•  8.6 Vector Potential and the Boundary Value Point ofView

 

Magnetization

•  9.1 Magnetization Density

•  9.2 Laws and Continuity Conditions with Magnetization

•  9.3 Permanent Magnetization

•  9.4 Magnetization Constitutive Laws

•  9.5 Fields In The Presence Of Magnetically Linear Insulating Materials

•  9.6 Fields in Piece-Wise Uniform Magnetically Linear Materials

•  9.7 Magnetic Circuits

 

Magnetoquasistatic Relaxation and Diffusion

•  10.1 Magnetoquasistatic Electric Fields in Systems of PerfectConductors

•  10.2 Nature of Fields Induced in Finite Conductors

•  10.3 Diffusion of Axial Magnetic FIelds Through ThinConductors

•  10.4 Diffusion of Transverse Magnetic FieldsThrough Thin Conductors

•  10.5 Magnetic Diffusion Laws

•  10.6 Magnetic Diffusion Transient Response

•  10.7 Skin Effect

 

Energy, Power Flow, and Forces

•  11.1 Integral and Differential Conservation Statements

•  11.2 Poynting’s Theorem

•  11.3 Ohmic Conductors With Linear Polarization andMagnetization

•  11.4 Energy Storage

•  11.5 Electromagnetic Dissipation

•  11.6 Electrical Forces on Macroscopic Media

•  11.7 Macroscopic Magnetic Forces

•  11.8 Forces on Microscopic Electric and Magnetic Dipoles

•  11.9 Macroscopic Force Densities

 

Electrodynamic Fields: The Superposition Integral Point of View

•  12.1 Electrodynamic Fields and Potentials

•  12.2 Electrodynamic Fields of Source Singularities

•  12.3 Superposition Integral for Electrodynamic Fields

•  12.4 Antenna Radiation Fields in the Sinusoidal Steady State

•  12.5 Complex Poynting’s Theorem and Radiation Resistance

•  12.6 Periodic Sheet-Source Fields: Uniform and Nonuniform PlaneWaves

•  12.7 Electrodynamic Fields in the Presence of PerfectConductors

 

Electrodynamic Fields: The Boundary Value Point of View

•  13.1 Introduction to TEM Waves

•  13.2 Two-Dimensional Modes Between Parallel Plates

•  13.3 TE and TM Standing Waves Between Parallel Plates

•  13.4 Rectangular Waveguide Modes

•  13.5 Dielectric Waveguides: Optical Fibers

 

One-Dimensional Wave Dynamics

•  14.1 Distributed Parameter Equivalents and Models

•  14.2 Transverse Electromagnetic Waves

•  14.3 Transients on Infinite Transmission Lines

•  14.4 Transients on Bounded Transmission Lines

•  14.5 Transmission Lines in the Sinusoidal Steady State

•  14.6 Reflection Coefficient Representation of Transmission Lines

•  14.7 Distributed Parameter Equivalents and Models with Dissipation

•  14.8 Uniform and TEM Waves in Ohmic Conductors (R = 0)

•  14.9 Quasi-One-Dimensional Models (G = 0)

 

Overview of Electromagnetic Fields

•  15.1 Source and Material Configurations

•  15.2 Macroscopic Media

•  15.3 Characteristic Times, Physical Processes, andApproximations

•  15.4 Energy, Power, and Force

 

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