Phys/Elec: 312: Advanced Electromagnetism
Spring 2022
Topics Covered in Lectures
Lecture Number |
Date |
Content |
Corresponding Reading material |
1 |
Feb. 15 |
Review of electrostatics: Coulomb’s law, electric
field of one or more point charges, electric field of a continuous
distribution of charges, divergence of the electric field and Gauss’ law,
curl of the electric field and the electric potential, Poisson’s equation for
the electric potential, multipole expansion of the electric field, electric
dipole moment, and polarization of dielectric media, electric potential for a
polarized dielectric medium, volume and surface bound charge densities, the
displacement field and Gauss’s law in a dielectric, linear dielectric media
and their electric susceptibility and permittivity tensors, isotropic,
stationary, and homogeneous dielectric media, permittivity and dielectric
constant. |
Pages 59-86, 154-156, & 172-202 of the textbook (Griffith’s Introduction to Electrodynamics, 4th Edition) |
2 |
Feb. 17 |
Review of magnetostatics: Magnetic force on a moving point charge and a continuous distribution of moving charges, current density, charge conservation and the continuity equation, magnetic field due to a current distribution and the Biot-Savart’s law, curl of the magnetic field and Ampere’s law, divergence of the magnetic field and the vector potential, gauge transformations and the Poisson’s equation for the vector potential, multipole expansion of the vector potential, lack of magnetic monopoles, magnetic dipole moment and magnetization of dielectric material, volume and surface bound current densities, magnetic induction field, and Ampere’s law in a dielectric medium. Linear magnetic material, magnetic susceptibility and permeability tensors, isotropic, stationary, and homogenous magnetic material. |
Pages 211-290 of the textbook |
3 |
Feb. 22 |
Review of electrodynamics: Electromotive force and
Faraday’s law, Maxwell’s equation in vacuum, EM filed in a dielectric medium,
the polarization current and Maxwell’s equations in a dielectric medium |
Pages 300-325, 336-342 &
344-346 of the textbook |
4 |
Feb.24 |
Integral form of Maxwell’s equations in a dielectric
medium, boundary conditions on the interface of two dielectric media, force
applied by an external electric field on a perfect electric dipole |
Pages 346-348 & 171of the
textbook |
5 |
Mar. 01 |
Interaction (potential) energy of an electric dipole placed in a magnetic field, the energy density of a electric field in a linear and isotropic medium |
Pages 197-202 & 294-295 of
the textbook |
6 |
Mar. 03 |
The energy density of a magnetic field in a linear, isotropic, and stationary medium; Conservation laws: Local conservation of electric charges and its continuity equation, Poynting theorem, local conservation of EM energy and its continuity equation |
Pages 332-336 & 360-364 of the textbook |
7 |
Mar. 08 |
EM force density, Maxwell’s stress tensor, and its physical interpretation |
Pages 336-367 of the textbook |
Snow break |
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8 |
Mar. 15 |
Momentum of the EM fields and its conservation, the continuity equation for local conservation of momentum, Angular momentum stored in EM fields |
Pages 367-377 of the textbook |
9 |
Mar. 17 |
EM Waves: Derivation of the wave equation for a vibrating string, d’Alembert’s solution of the wave equation in 1+1 dimensions, solution of the wave equation in 1+1 dimensions using Fourier transform |
Pages 387-390 of the textbook |
10 |
Mar. 22 |
Sinusoidal waves and their complex wave functions, scattering problem for an infinite vibrating string consisting of two uniform halves with different mass densities |
Pages 390-396 of the textbook |
11 |
Mar. 24 |
Polarization, transverse and longitudinal waves; EM waves: Wave equation for EM fields in vacuum, monochromatic plane waves, their wave vector and polarization |
Pages 396-403 of the textbook |
Midterm Exam 1 |
Mar. 26 |
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|
12 |
Mar. 29 |
Energy density, Poynting vector, intensity, momentum density, and radiation pressure of a plane wave; EM waves in a stationary, linear, isotropic, and homogeneous dielectric medium; scattering from a planar interface separating a pair of dielectric media |
Pages 403-411 of the textbook |
13 |
Mar. 31 |
Incidence plane, Snell’s law, TE and TM waves |
Pages 411-413 of the textbook |
14 |
Apr. 05 |
Fresnel’s equations, Brewster’s angle, Reflection and transmission coefficients for TM waves, EM wave propagation in a conductor |
Pages 414-418 of the textbook |
15 |
Apr. 07 |
EM wave propagation in a conductor; Reflection of a normally incident plane wave from a conducting surface, Dispersion |
Pages 418-425 of the textbook |
Spring Break |
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|
|
16 |
Apr. 19 |
Complex permittivity and refractive index, attenuation and gain coefficients, Cauchy’s dispersion formula |
Pages 425-429 of the textbook |
17 |
Apr. 21 |
Wave guides: Boundary conditions, EM waves for a straight wave guide, Helmholtz equations and boundary conditions for a straight wave guide, TE, TM, and TEM waves in a straight wave guide |
Pages 430-432 of
the textbook |
18 |
Apr. 26 |
Solutions of the Helmholtz equation for a TE wave propagating in a rectangular waveguide by separation of variables, cut-off frequencies and the TEmn modes, phase and group velocities; Scalar and vector potentials in electrodynamics |
Pages 433-435 &
553-555 of the textbook |
19 |
Apr. 28 |
Gauge symmetry of electrodynamics, Lorentz gauge and the inhomogeneous wave equations for scalar and vector potentials, Retarded and advanced potentials, Jefimenko’s equations |
Pages 556-559 &
561-568 of the textbook |
Bayram Holidays |
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|
|
20 |
May 10 |
Retarded (Lienard-Wiechart) potentials for a moving point charge & the EM field of a moving point charge; Basic idea of radiation, radiation from an electric dipole, implication for Bohr’s model of Hydrogen atom; Special Relativity: Space, time, events, and inertial observers, Michelson-Morley’s experiment, ether shield, FitzGerald-Lorentz contraction |
Pages 569-580 &
441-449 of the textbook |
21 |
May12 |
Galilean Principle of relativity and Einstein formulation
of Special Theory of Relativity. The implications of the postulate that c is
frame-independent: Relativity of the simultaneity, time dilation, and Lorentz
contraction; Galilean transformations |
Pages 479-495 of the textbook |
Midterm Exam 2 |
May 14 |
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|
22 |
May 17 |
Lorentz transformations, Einstein’s velocity addition formula, Euclidean geometry of space and time in Newtonian mechanics, 4-vectors and Einstein’s summation convention, Minkowski inner product and metric, Minkowski spacetime, 4-vectors and Einstein’s summation convention, Causal structure of Minkowski spacetime |
Pages 495-509 of the textbook |
23 |
May 24 |
Proper time, proper velocity, proper momentum, and energy of a relativistic free particle, relativistic conservation of momentum and energy, the mass to energy conversion in a decay process; Relativistic invariance of the electric charge and the current 4-vector |
Pages 509-519 & 542-543 of the textbook |
24 |
May 26 |
Covariant and contravariant 4-vectors and 4-vector fields, scalar fields, relativistic invariance of the Lorentz-gauge condition and D’Alembertian, Maxwell’s equation, Covariant and contravariant 4-vector potentials and electromagnetic field tensors, gauge transformation rule for the 4-vector potential, the Lorentz transformation rule for the electric and magnetic fields, dual electromagnetic field tensor and a manifestly covariant form of Maxwell’s equations. |
Pages 539-547 of
the textbook |
Note:
The pages from the textbook listed above may not include some of the material
covered in the lectures.