6.013 | Fall 2005 | Undergraduate
Electromagnetics and Applications


The calendar below provides information on the course’s lecture (L), recitation (R), and quiz (Q) sessions.

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
R1 Review of vector and integral calculus; cartesian, cylindrical, and spherical coordinate systems; ej(ωt-kz) complex notation; gradient, curl, and divergence Problem set 1 out

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

R2 Simple problems using superposition and integral forms of Gauss’ and Ampere’s laws with simple spatial distributions of volume charge density and volume current density  
L2 Derive boundary conditions; apply boundary conditions to surface charge and surface current problems Problem set 2 out
R3 Boundary condition problems, e.g., perfectly conducting sphere or cylinder surrounding point or line charge or line current Problem set 1 due

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

R4 Problem solutions using differential form of Maxwell’s equations: surface and volume charged or current carrying planar layer, cylinder and sphere  
L4 The electric field, electric scalar potential, and the gradient; Poisson’s and Laplace’s equations; potential of point charge; Coulomb superposition integral Problem set 3 out
R5 The electric dipole (potential and electric field); simple problems using the Coulomb superposition integral (line charge, ring of line charge, disk of surface charge) Problem set 2 due
L5 Method of images  
R6 Method of images problems with planes, cylinders, and spheres  

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)

Problem set 4 out

Capacitance, resistance, inductance, and charge relaxation problems in cartesian, cylindrical, and spherical geometries

Demo: H/M 7.7.1 relaxation of charge on particle in ohmic conductor (video); supplement: Kelvin’s water dynamos (video)

Problem set 3 due
L7 Conservation of charge boundary condition; maxwell capacitor; magnetic dipoles and circuits; reluctance  
II. Plane waves
L8 Wave equation; Poynting’s theorem  

Sinusoidal steady state; normal incidence on a perfect conductor and a dielectric

Demo: plane wave movies

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 Problem set 5 out

Snell’s law: brewster and critical angles; effects of ohmic loss; skin-depth

Demo: laser and prism Brewster’s angle, critical angle

Problem set 4 due
R10 Lasers; applications to optics: polarization by reflection; totally reflecting prisms; fiber optics-straight light pipe, bent fiber  
R11 Lasers; optical devices

Problem set 5 due

Problem set 6 out

III. Transmission lines and waveguides

Parallel plate transmission lines; wave equation; sinusoidal steady state

Demo: H/M 13.1.1 visualization of standing waves

R12 Transmission line sinusoidal steady state problems with short circuit, open circuit, and loaded ends; short-line limits as circuit approximations to capacitors and inductors  

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

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

R13 Quiz 1 review  
Q1 Quiz 1  
R14 Impedance and VSWR problems using the Smith chart; single-stub tuner  

Wave equations (lossless); transient waves on transmission lines

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

Problem set 7 out

Transient wave driven and initial value problems

Demo: transient wave movies

Problem set 6 due
L13 Reflections from ends; driven and initial value problems  

Waveguide fields; surface charge and current; calculation and sketching of electric and magnetic field lines

Demo: show plots of electric and magnetic field lines for various waveguide modes

L14 Rectangular waveguides; TM and TE modes; cut-off Problem set 8 out
R17 Cavity resonators; group and phase velocity; dispersion relations; lasers Problem set 7 due
IV. Fields and forces

Dielectric waveguides

Demo: evanescent waves

R18 Force problems in capacitive and inductive systems  

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)

R19 Ohm’s law for moving media; Faraday’s disk (homopolar generator); torque; equivalent circuit

Problem set 8 due

Problem set 9 out


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

R20 Quiz 2 review  
Q2 Quiz 2  
R21 Torque-speed characteristics of rotating machines  
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 Problem set 10 out
R22 Electric and magnetic fields from a point electric dipole; far-field solution; radiation resistance; effective dipole length; antenna gain Problem set 9 due

2 element array; broad side and end-fire arrays

Demo: radiation patterns

Problem set 11 out

Element and array factors; N dipole array; beam steering

Demo: radiation patterns/computer simulations

Problem set 10 due
L21 Transmitting and receiving antennas; wireless and optical communications  
R24 Wireless and optical communication problems  
VI. Acoustics
L22 Acoustic waves  
R25 Acoustic wave boundary value problems Problem set 11 due
L23 Course review  
Learning Resource Types
assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes