Supplemental Resources

Electromagnetic Fields and Energy

Hermann A. Haus, James R. Melcher, Markus Zahn, and Manuel L. Silva

MIT OpenCourseWare is pleased to make this textbook available online. Published in 1989 by Prentice-Hall, this book is a useful resource for educators and self-learners alike. The text is aimed at those who have seen Maxwell's equations in integral and differential form and who have been exposed to some integral theorems and differential operators. A hypertext version of this textbook can be found here. An accompanying set of video demonstrations is available below.

These video demonstrations convey electromagnetism concepts. The demonstrations are related to topics covered in the textbook. They were prepared by Markus Zahn, James R. Melcher, and Manuel L. Silva and were produced by the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology.

The purpose of these demonstrations is to make mathematical analysis of electromagnetism take on physical meaning. Based on relatively simple configurations and arrangements of equipment, they make a direct connection between what has been analytically derived and what is observed. They permit the student to observe physically what has been described symbolically. Often presented with a plot of theoretical predictions that are compared to measured data, these demonstrations give the opportunity to test the range of validity of the theory and present a quantitative approach to dealing with the physical world.

The short form of these videos contains the demonstrations only. The long form also presents theory, diagrams, and calculations in support of the demonstrations.

These videos are used in the courses 6.013J/ESD.013J and 6.641.

Electromagnetic Fields and Energy Textbook Components with Video Demonstrations

TEXTBOOK CONTENTS	DEMONSTRATION TOPICS	VIDEOS - SHORT FORM	VIDEOS - LONG FORM
Front-End Matter
Dedication (PDF) Preface (PDF) Table of contents (PDF) Appendix 1: Vector operations (PDF) Vectors Vector addition Definition of scalar product Definition of vector product The scalar triple product The double cross-product Appendix 2: Line and surface integrals and proof that curl is a vector (PDF) Line integrals Surface integrals Proof that the curl operation results in a vector
Chapter 1: Maxwell's integral laws in free space (PDF)
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 distribution 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	1.3.1, 1.5.1: Coulomb's force law and measurements of charge	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 27.1MB)
	1.4.1: Magnetic field of a line current	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 14.5MB)
	1.6.1: Voltmeter reading induced by magnetic induction	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 15.6MB)
Chapter 2: Maxwell's differential laws in free space (PDF)
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
Chapter 3: Introduction to electroquasistatics and magnetoquasistatics (PDF)
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
Chapter 4: Electroquasistatic fields: the superposition integral point of view (PDF)
4.0 Introduction 4.1 Irrotational field represented by scalar potential: the gradient operator and the 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	4.7.1: Charge induced in ground plane by overhead conductor	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 19.6MB)
Chapter 5: Electroquasistatic fields from the boundary value point of view (PDF)
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	5.5.1: Capacitance attenuator	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 26MB)
Chapter 6: Polarization (PDF)
6.0 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	6.6.1: An artificial dielectric	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 24.9MB)
Chapter 7: Conduction and electroquasistatic charge relaxation (PDF)
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 7.9 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	7.5.1: Distribution of unpaired charge (Courtesy of Education Development Center, Inc. Used with permission.)	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 10.8MB)
	7.5.2: Rotation of an insulating rod in a steady current (Courtesy of Education Development Center, Inc. Used with permission.)	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 12.8MB)
	7.7.1: Relaxation of charge on particle in Ohmic conductor (Courtesy of Education Development Center, Inc. Used with permission.) 7.7.1 Supplement: Van de Graaff and Kelvin generators (Courtesy of Education Development Center, Inc. Used with permission.)	Streaming: (RM - 56K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 13.4MB)
	7.7.2: Electrostatic precipitation	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 44.6MB)
Chapter 8: Magnetoquasistatic fields: superposition integral and boundary value points of view (PDF)
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 potential for two-dimensional fields Vector potential for axisymmetric fields in spherical coordinates Boundary value solution by "Inspection" Method of images Two-dimensional boundary value problems 8.7 Summary	8.2.1: Field of a circular cylindrical solenoid	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 16.7MB)
	8.2.2: Field of square pair of coils	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 20.6MB)
	8.4.1: Surface used to define the flux linkage	Streaming: (RM - 56K) (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 19.7MB)
	8.5.1: Field and inductance of a spherical coil	Streaming: (RM - 56K) (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 18.3MB)
	8.6.1: Surface currents induced in ground plane by overhead conductor	Streaming: (RM - 56K) (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 20.8MB)
	8.6.2: Inductive attenuator	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 35.6MB)
Chapter 9: Magnetization (PDF)
9.0 Introduction 9.1 Magnetization density 9.2 Laws and continuity conditions with magnetization Faraday's law including magnetization Magnetic flux density Terminal voltage with magnetization 9.3 Permanent magnetization 9.4 Magnetization constitutive laws 9.5 Fields in the presence of magnetically linear insulating materials Inductance in the presence of linearly magnetizable materials Induced magnetic charge: demagnetization 9.6 Fields in piece-wise uniform magnetically linear materials Excitation in region of high permeability Excitation in region of low permeability 9.7 Magnetic circuits Electrical terminal relations and characteristics 9.8 Summary	9.4.1: Measurement of B-H characteristic	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 17.8MB)
Chapter 10: Magnetoquasistatic relaxation and diffusion (PDF)
10.0 Introduction 10.1 Magnetoquasistatic electric fields in systems of perfect conductors 10.2 Nature of fields induced in finite conductors 10.3 Diffusion of axial magnetic fields through thin conductors 10.4 Diffusion of transverse magnetic fields through thin conductors Response to a step in applied field 10.5 Magnetic diffusion laws Physical interpretation 10.6 Magnetic diffusion transient response Product solutions to the one-dimensional diffusion equation 10.7 Skin effect 10.8 Summary	10.0.1: Nonuniqueness of voltage in a magnetoquasistatic (MQS) system	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 16MB)
	10.2.1: Edgerton's boomer	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 58.8MB)
	10.4.1: Currents induced in a conducting shell	Streaming: (RM - 56K) (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 17.1MB)
	10.7.1: Skin effect	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 24.7MB)
Chapter 11: Energy, power flow, and forces (PDF)
11.0 Introduction Power flow in a circuit Overview 11.1 Integral and differential conservation statements 11.2 Poynting's theorem Systems composed of perfect conductors and free space 11.3 Ohmic conductors with linear polarization and magnetization An alternative conservation theorem for electroquasistatic systems Poynting power density related to circuit power input Poynting flux and electromagnetic radiation 11.4 Energy storage Energy densities Energy storage in terms of terminal variables 11.5 Electromagnetic dissipation Energy conservation for temporarily periodic systems Induction heating Dielectric heating Hysteresis losses 11.6 Electrical forces on macroscopic media 11.7 Macroscopic magnetic forces Reciprocity conditions Finding the coenergy Evaluation of the force The torque of electrical origin 11.8 Forces on macroscopic electric and magnetic dipoles Force on an electric dipole Force on electric charge derived from energy principle Force on a magnetic charge and magnetic dipole Comparison of Coulomb's force to the force on a magnetic dipole 11.9 Macroscopic force densities The Lorentz force density The Kelvin polarization force density The Kelvin magnetization force density Alternative force densities 11.10 Summary	11.6.2: Force on a liquid dielectric (Courtesy of Education Development Center, Inc. Used with permission.)	Streaming: (RM - 56K) (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 18.3MB)
	11.7.1: Steady state magnetic levitation	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 36MB)
Chapter 12: Electrodynamic fields: the superposition integral point of view (PDF)
12.0 Introduction 12.1 Electrodynamic fields and potentials Superposition principle Continuity conditions 12.2 Electrodynamic fields of source singularities Potential of a point charge Electric dipole field Electric dipole in the sinusoidal steady state The far-field and uniformly polarized plane waves Magnetic dipole field 12.3 Superposition integral for electrodynamic fields Transient response Sinusoidal steady state response 12.4 Antennae radiation fields in the sinusoidal steady state Distributed current distribution Arrays Dipoles in broadside array Dipoles in end-fire array Finite dipoles in end-fire array Gain 12.5 Complex Poynting's theorem and radiation resistance Complex Poynting's theorem Radiation resistance 12.6 Periodic sheet-source fields: uniform and nonuniform plane waves Transverse magnetic (TM) fields Product solutions to the Helmholtz equation Transverse electric (TE) fields 12.7 Electrodynamic fields in the presence of perfect conductors Method of images Quarter-wave antenna above a ground-plane Two-element array over ground plane Ground-plane with reflector Boundaries at the nodes of standing waves 12.8 Summary
Chapter 13: Electrodynamic fields: the boundary value point of view (PDF)
13.0 Introduction 13.1 Introduction to transverse electromagnetic (TEM) waves The magnetoquasistatic (MQS) limit The MQS approximation The electroquasistatic (EQS) limit The EQS approximation 13.2 Two-dimensional modes between parallel-plates 13.3 Transverse (TE) and transverse magnetic (TM) standing waves between parallel plates 13.4 Rectangular waveguide modes 13.5 Dielectric waveguides: optical fibers 13.6 Summary	13.1.1: Visualization of standing waves	Streaming: (RM - 80K) (RM - 220K)	Streaming: (RM - 56K) (RM - 220K) Downloadable: (MP4 - 23.4MB)
Chapter 14: One-dimensional wave dynamics (PDF)
14.0 Introduction 14.1 Distributed parameter equivalents and models Plane waves Ideal transmission line Quasi-one-dimensional models 14.2 Transverse electromagnetic waves No TEM fields in hollow pipes Power-flow and energy storage 14.3 Transients on infinite transmission lines Response to initial conditions 14.4 Transients on bounded transmission lines Matching 14.5 Transmission lines in the sinusoidal steady state Transmission line impedance 14.6 Reflection coefficient representation of transmission lines Smith chart Standing wave ratio Admittance in the reflection-coefficient plane 14.7 Distributed parameter equivalents and models with dissipation 14.8 Uniform and TEM waves in Ohmic conductors Displacement current much greater than conduction current Conduction current much greater than displacement current 14.9 Quasi-one-dimensional models Charge diffusion transmission-line Skin-depth small compared to all dimensions of interest 14.10 Summary
Chapter 15: Overview of electromagnetic fields (PDF)
15.0 Introduction 15.1 Source and material configurations Incremental dipoles Planar periodic configurations Cylindrical and spherical Fields between plane parallel plates Axisymmetric (coaxial) fields TM and TE fields with longitudinal boundary conditions Cylindrical conductor pair and conductor plane 15.2 Macroscopic media Source representation of macroscopic media Material idealizations The relativity of perfection 15.3 Characteristic times, physical processes, and approximations Self-consistency of approximate laws Similitude and Maxwell's equations Characteristic times and lengths 15.4 Energy, power, and force Energy and quasistatics

Electromagnetic Fields and Energy Solutions Manual

Electromagnetic Fields and Energy Solutions Manual as one file (PDF - 12.7MB)

Title page and Preface (PDF)

CHAPTERS	FILES
Chapter 1, pp. 1.1-1.19	(PDF)
Chapter 2, pp. 2.1-2.15	(PDF)
Chapter 3, pp. 3.1-3.8	(PDF)
Chapter 4, pp. 4.1-4.38	(PDF - 1.3MB)
Chapter 5, pp. 5.1-5.35	(PDF - 1.6MB)
Chapter 6, pp. 6.1-6.23	(PDF)
Chapter 7, pp. 7.1-7.32	(PDF - 1.3MB)
Chapter 8, pp. 8.1-8.25	(PDF)
Chapter 9, pp. 9.1-9.30	(PDF - 1.1MB)
Chapter 10, pp. 10.1-10.35	(PDF - 1.1MB)
Chapter 11, pp. 11.1-11.36	(PDF - 1.1MB)
Chapter 12, pp. 12.1-12.20	(PDF)
Chapter 13, pp. 13.1-13.22	(PDF)
Chapter 14, pp. 14.1-14.20	(PDF)
Chapter 15, pp. 15.1-15.8	(PDF)

Recommended Citation

For any use or distribution of this textbook, video demonstrations, and solutions manual, please cite as follows:

Textbook

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

Video demonstrations

Markus Zahn, James R. Melcher, and Manuel L. Silva, Selected Demonstrations from Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-NonCommercial-Share Alike

Solutions manual

Haus, Hermann A., and James R. Melcher. Solutions Manual for 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, 1990. ISBN: 9780132489805. License: Creative Commons Attribution-NonCommercial-Share Alike