| 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 |
| L1 |
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
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| 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 |
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| 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 |
| L3 |
Divergence and Stokes' theorems; Maxwell's equations in differential form; electroquasistatics and magnetoquasistatics; potential and the gradient operator
Demo: H/M 10.0.1 nonuniqueness of voltage in an MQS system
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| R4 |
Problem solutions using differential form of Maxwell's equations: surface and volume charged or current carrying planar layer, cylinder and sphere |
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| 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 |
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| R6 |
Method of images problems with planes, cylinders, and spheres |
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| L6 |
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
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Problem set 4 out |
| R7 |
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)
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Problem set 3 due |
| L7 |
Conservation of charge boundary condition; maxwell capacitor; magnetic dipoles and circuits; reluctance |
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| II. Plane waves |
| L8 |
Wave equation; Poynting's theorem |
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| R8 |
Sinusoidal steady state; normal incidence on a perfect conductor and a dielectric
Demo: plane wave movies
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| L9 |
Oblique incidence on a perfect conductor; TM waves with oblique incidence on lossless media described by ε and µ; reflection and transmission; TE waves with oblique incidence on lossless media |
Problem set 5 out |
| R9 |
Snell's law: brewster and critical angles; effects of ohmic loss; skin-depth
Demo: laser and prism Brewster's angle, Critical angle
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Problem set 4 due |
| R10 |
Lasers; applications to optics: polarization by reflection; totally reflecting prisms; fiber optics-straight light pipe, bent fiber |
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| R11 |
Lasers; optical devices |
Problem set 5 due
Problem set 6 out
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| III. Transmission lines and waveguides |
| L10 |
Parallel plate transmission lines; wave equation; sinusoidal steady state
Demo: H/M 13.1.1 visualization of standing waves
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| 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 |
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| L11 |
Gamma plane; Smith chart; VSWR; λ/4 transformer
Demo: V(z,t), I(z,t) movies
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| R13 |
Quiz 1 review |
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| Q1 |
Quiz 1 |
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| R14 |
Impedance and VSWR problems using the Smith chart; single-stub tuner |
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| L12 |
Wave equations (lossless); transient waves on transmission lines
Demo: H/M 14.4.1 transmission line matching, reflection, and quasistatic charging
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Problem set 7 out |
| R15 |
Transient wave driven and initial value problems
Demo: transient wave movies
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Problem set 6 due |
| L13 |
Reflections from ends; driven and initial value problems |
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| R16 |
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
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| L14 |
Rectangular waveguides; transverse magnetic (TM) and transverse electric (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 |
| L15 |
Dielectric waveguides
Demo: evanescent waves
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| R18 |
Force problems in capacitive and inductive systems |
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| L16 |
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)
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| R19 |
Ohm's law for moving media; Faraday's disk (homopolar generator); torque; equivalent circuit |
Problem set 8 due
Problem set 9 out
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| L17 |
Synchronous rotating machines
Film: Synchronous Machines
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| L18 |
Self-excited electric and magnetic machines
Demo: H/M 7.7.1 van de Graaff and Kelvin generators (video); self-excited commutator machines
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| R20 |
Quiz 2 review |
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| Q2 |
Quiz 2 |
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| R21 |
Torque-speed characteristics of rotating machines |
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| 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 |
| L20 |
2 element array; broad side and end-fire arrays
Demo: radiation patterns
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Problem set 11 out |
| R23 |
Element and array factors; N dipole array; beam steering
Demo: radiation patterns/computer simulations
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Problem set 10 due |
| L21 |
Transmitting and receiving antennas; wireless and optical communications |
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| R24 |
Wireless and optical communication problems |
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| VI. Acoustics |
| L22 |
Acoustic waves |
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| R25 |
Acoustic wave boundary value problems |
Problem set 11 due |
| L23 |
Course review |
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