6.013 | Fall 2005 | Undergraduate

Electromagnetics and Applications

Lecture Notes

Some of the lecture notes were prepared in LaTeX by Alan Dunn, a former MIT student. He used Prof. Zahn’s handwritten notes to produce them.

H/M = Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207.

I. Maxwell’s equations

Coulomb-Lorentz force law; Maxwell’s equations in integral form; simple electric and magnetic field solutions using Gauss’ and Ampere’s laws for point, line, and surface charges and currents; superposition; simple cylindrical and spherical source problems

Demos: H/M 10.2.1 - Edgerton’s Boomer

L2 Derive boundary conditions; apply boundary conditions to surface charge and surface current problems (PDF)

Divergence and Stokes’ theorems; Maxwell’s equations in differential form; electroquasistatics and magnetoquasistatics (MQS); potential and the gradient operator

Demo: H/M 10.0.1 nonuniqueness of voltage in an MQS system

L4 The electric field, electric scalar potential, and the gradient; Poisson’s and Laplace’s equations; potential of point charge; Coulomb superposition integral (PDF)
L5 Method of images (PDF)

Lecture 6

Media: dielectric, conducting, and magnetic constitutive laws; charge relaxation

Demos: H/M 6.6.1 artificial dielectric; 9.4.1 measurement of B-H characteristic (magnetic hysteresis loop)

Lecture 7

Conservation of charge boundary condition; Maxwell capacitor; magnetic dipoles and circuits; reluctance

(PDF - 1.2 MB)
II. Plane waves
L8 Wave equation; Poynting’s theorem (PDF)
L9 Oblique incidence on a perfect conductor; transverse magnetic (TM) waves with oblique incidence on lossless media described by ε and µ; reflection and transmission; transverse electric (TE) waves with oblique incidence on lossless media (PDF)
III. Transmission lines and waveguides

Parallel plate transmission lines; wave equation; sinusoidal steady state

Demo: H/M 13.1.1 visualization of standing waves


Gamma plane; Smith chart; voltage standing wave ratio (VSWR); λ/4 transformer

Demo: V(z,t), I(z,t) movies

(PDF - 2.6 MB)

Lecture 12

Wave equations (lossless); transient waves on transmission lines

Demo: H/M 14.4.1 transmission line matching, reflection, and quasistatic charging

Lecture 13

Reflections from ends; driven and initial value problems

(PDF - 2.5 MB)
L14 Rectangular waveguides; TM and TE modes; cut-off (PDF)
IV. Fields and forces

Dielectric waveguides

Demo: evanescent waves


Lecture 16

Energy in electric and magnetic fields; principle of virtual work to find electric and magnetic forces; magnetic circuit problems

Demo: H/M 11.6.2 force on a dielectric material (video)

Lecture 17

Synchronous rotating machines

Film: Synchronous Machines


Self-excited electric and magnetic machines

Demo: H/M 7.7.1 van de Graaff and Kelvin generators (video); self-excited commutator machines

(PDF - 1.3 MB)
V. Antennas and radiation
L19 Radiation by charges and currents; setting the gauge; Lorentz gauge; superposition integral solutions for scalar and vector potentials; radiation from a point electric dipole; receiving antenna properties (PDF)

2 element array; broad side and end-fire arrays

Demo: radiation patterns

(PDF - 1.1 MB)
L21 Transmitting and receiving antennas; wireless and optical communications (PDF - 1.5 MB)
VI. Acoustics
L22 Acoustic waves (PDF - 2.5 MB)
L23 Course review (PDF - 1.2 MB)
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes