MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following citation format: Haus, Hermann A., and James R. Melcher, Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). Also available from Prentice-Hall: Englewood Cliffs, NJ, 1989. ISBN: 9780132490207. License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/termsCONTENTS PREFACE 1 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 Density Singular Charge Distributions. Gauss’ Continuity Condition. 1.4 Ampere’s Integral Law Singular Current Distributions. Ampere’s Continuity Condition. 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. 1.8 Summary 2 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 Charge Conservation 2.4 The Curl Operator 2.5 Stokes’ Integral Theorem 2.6 Differential Laws of Ampere and Faraday 2.7 Visualization of Fields and the Divergence and Curl 2.8 Summary of Maxwell’s Differential Laws and Integral Theorems 3 Introduction to Electroquasistatics and Magnetoquasistatics 3.0 Introduction 3.1 Temporal Evolution of World Governed by Laws of Maxwell, Lorentz, and Newton 3.2 Quasistatic Laws 3.3 Conditions for Fields to be Quasistatic 3.4 Quasistatic Systems 3.5 Overview of Applications 3.6 Summary 14 Electroquasistatic Fields: The Superposition Integral Point of View 4.0 Introduction 4.1 Irrotational Field Represented by Scalar Potential: The Gradient Operator and Gradient Integral Theorem Visualization of Two-Dimensional Irrotational Fields. 4.2 Poisson’s Equation 4.3 Superposition Principle 4.4 Fields Associated with Charge Singularities Dipole at the Origin. Pair of Charges at Infinity Having Equal Magnitude and Opposite Sign. Other Charge Singularities. 4.5 Solution of Poisson’s Equation for Specified Charge Distributions Superposition Integral for Surface Charge Density. Superposition Integral for Line Charge Density. Two-Dimensional Charge and Field Distributions. Potential of Uniform Dipole Layer. 4.6 Electroquasistatic Fields in the Presence of Perfect Conductors Capacitance. 4.7 Method of Images 4.8 Charge Simulation Approach to Boundary Value Problems 4.9 Summary 5 Electroquasistatic Fields from the Boundary Value Point of View 5.0 Introduction 5.1 Particular and Homogeneous Solutions to Poisson’s and Laplace’s Equations Superposition to Satisfy Boundary Conditions. Capacitance Matrix. 5.2 Uniqueness of Solutions of Poisson’s Equation 5.3 Continuity Conditions 5.4 Solutions to Laplace’s Equation in Cartesian Coordinates 5.5 Modal Expansions to Satisfy Boundary Conditions 5.6 Solutions to Poisson’s Equation with Boundary Conditions 5.7 Solutions to Laplace’s Equation in Polar Coordinates 5.8 Examples in Polar Coordinates Simple Solutions. Azimuthal Modes. Radial Modes. 5.9 Three Solutions to Laplace’s Equation in Spherical Coordinates 5.10 Three-Dimensional Solutions to Laplace’s Equation Cartesian Coordinate Product Solutions. Modal Expansion in Cartesian Coordinates. Modal Expansion in Other Coordinates. 5.11 Summary 6 Polarization 26.0 Introduction 6.1 Polarization Density 6.2 Laws and Continuity Conditions with Polarization Polarization Current Density and Ampere’s Law. Displacement Flux Density. 6.3 Permanent Polarization 6.4 Polarization Constitutive Laws 6.5 Fields in the Presence of Electrically Linear Dielectrics Capacitance. Induced Polarization Charge. 6.6 Piece-wise Uniform Electrically Linear Dielectrics Uniform Dielectrics. Piece-wise Uniform Dielectrics. 6.7 Smoothly Inhomogeneous Electrically Linear Dielectrics 6.8 Summary 7 Conduction and Electroquasistatic Charge Relaxation 7.0 Introduction 7.1 Conduction Constitutive Laws Ohmic Conduction. Unipolar Conduction. 7.2 Steady Ohmic Conduction Continuity Conditions. Conductance. Qualitative View of Fields in Conductors. 7.3 Distributed Current Sources and Associated Fields Distributed Current Source Singularities. Fields Associated with Current Source Singularities. Method of Images. 7.4 Superposition and Uniqueness of Steady Conduction Solutions Superposition to Satisfy Boundary Conditions. The Conductance Matrix. Uniqueness. 7.5 Steady Currents in Piece-wise Uniform Conductors Analogy to Fields in Linear Dielectrics. Inside-Outside Approximations. 7.6 Conduction Analogs Mapping Fields That Satisfy Laplace’s Equation. 7.7 Charge Relaxation in Uniform Conductors Net Charge on Bodies Immersed in Uniform Materials. 7.8 Electroquasistatic Conduction Laws for Inhomogeneous Material Evolution of Unpaired Charge Density. Electroquasistatic Potential Distribution. Uniqueness. 37.9 Charge Relaxation in Uniform and Piece-Wise Uniform Systems Fields in Regions Having Uniform Properties. Continuity Conditions in Piece-Wise Uniform Systems. Nonuniform Fields in Piece-Wise Uniform Systems. 7.10 Summary 8 Magnetoquasistatic Fields: Superposition Integral and Boundary Value Points of View 8.0 Introduction Vector Field Uniquely Specified. 8.1 The Vector Potential And the Vector Poisson Equation Two-Dimensional Current and Vector Potential Distributions. 8.2 The Biot-Savart Superposition Integral Stick Model for Computing Fields of Electromagnet. 8.3 The Scalar Magnetic Potential The Scalar Potential of a Current Loop. 8.4 Magnetoquasistatic Fields in the Presence of Perfect Conductors Boundary Conditions and Evaluation of Induced Surface Current Density. Voltage at the Terminals of a Perfectly Conducting Coil. Inductance. 8.5 Piece-Wise Magnetic Fields 8.6 Vector Potential and the Boundary Value Point of View Vector
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