Phys/Elec: 312: Advanced Electromagnetism
Spring 2021
Topics Covered in Lectures
Lecture Number |
Date |
Content |
Corresponding Reading material |
1 |
Feb. 16 |
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, energy of a linear and isotropic dielectric medium. |
Pages 59-86, 154-156, & 172-202 of the textbook (Griffith’s Introduction to Electrodynamics, 4th Edition) |
2 |
Feb. 18 |
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. |
Pages 211-287 of the textbook |
3 |
Feb. 23 |
Linear magnetic material, magnetic susceptibility
and permeability tensors, isotropic, stationary, and homogenous magnetic
material. 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 287-290, 300-325, 336-342 &
344-346 of the textbook |
4 |
Feb.25 |
Integral form of Maxwell’s equations in a dielectric
medium, and boundary conditions on the interface of two dielectric media,
interaction (potential) energy of an electric dipole places in an electric
field |
Pages 346-348
& 171-172 of the textbook |
5 |
Mar. 02 |
Interaction (potential) energy of an electric dipole placed in a magnetic field, the energy density of the electric and magnetic fields inside a linear and isotropic medium |
Pages 197-202, 294-295 & 332-336 of the textbook |
6 |
Mar. 04 |
Conservation laws: Local conservation of electric
charges and its continuity equation, Poynting theorem, local conservation of
EM energy and its continuity equation, EM force density and Maxwell’s stress
tensor |
Pages 360-367 of the textbook |
7 |
Mar. 09 |
Interpretation of Maxwell’s stress tensor, momentum
stored in EM fields and its conservation, the continuity equation for local
conservation of momentum |
Pages 367-374 of the textbook |
8 |
Mar. 11 |
Angular momentum stored in EM fields. EM Waves:
Derivation of the wave equation for a vibrating string, d’Alembert’s solution
of the wave equation in 1+1 dimensions |
Pages 374-377 & 387-390 of the textbook |
Midterm Exam 1 |
Mar. 13 |
|
|
9 |
Mar. 16 |
Solution of the wave equation in 1+1 dimensions using Fourier transform, sinusoidal waves and their complex wave functions, scattering problem for an infinite vibrating string consisting of two uniform halves with different mass densities |
Pages 377-396 of the textbook |
10 |
Mar. 18 |
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 |
11 |
Mar. 23 |
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 |
12 |
Mar. 25 |
Snell’s
law, TE and TM waves, Fresnel’s equations |
Pages 411-414 of the textbook |
13 |
Mar. 30 |
Reflection
and transmission coefficients for TM waves, Brewster’s angle, EM wave
propagation in a conductor |
Pages 414-420 of the textbook |
14 |
Apr. 01 |
Reflection
of a normally incident plane wave from a conducting surface, Dispersion:
Complex permittivity and refractive index |
Pages 420-426 of the textbook |
Spring Break |
|
|
|
15 |
Apr. 13 |
Complex
permittivity, attenuation and gain coefficients, Cauchy’s dispersion
formula; Wave guides: Boundary conditions, EM waves for a straight wave guide
|
Pages 426-429 of the textbook |
16 |
Apr. 15 |
Helmholtz equations and boundary conditions for a
straight wave guide, TE, TM, and TEM waves in a straight wave guide, 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 |
Pages 430-435 of the textbook |
Midterm Exam 2 |
Apr. 18 |
|
|
17 |
Apr. 22 |
Scalar and vector potentials in electrodynamics, gauge symmetry of electrodynamics, Lorentz gauge and the inhomogeneous wave equations for scalar and vector potentials, Lorentz force law in terms of the scalar and vector potentials and the minimal coupling prescription |
Pages 553-561 of the textbook |
18 |
Apr. 27 |
Retarded and advanced potentials, Jefimenko’s equations |
Pages 561-567 of the textbook |
19 |
Apr. 29 |
Retarded
(Lienard-Wiechart) potentials for a moving point charge & the EM field of a moving point charge |
Pages 567-577 of the textbook |
20 |
May 04 |
Radiation
due to dynamical charge distributions, radiation by an oscillating electric
dipole. |
Pages 442-449 of the textbook |
21 |
May 06 |
Radiation by an arbitrary dynamical charge distribution, Larmor’s formula for power radiated by an accelerating charged particle |
Pages 453-457 of the textbook |
22 |
May 11 |
Inertial frames in classical Newtonian mechanics and principle of relativity, the apparent frame dependence of the Lorentz force, ether, ether wind, and the Michelson-Morley’s experiment, ether shield, FitzGerald-Lorentz contraction, and Einstein formulation of Special Theory of Relativity. The implications of the postulate that c is frame-independent: 1. Relativity of the simultaneity |
Pages 479-487 of the textbook |
Bayram Holidays |
|
|
|
23 |
May 18 |
Time
dilation and Lorentz contraction, Galilean and Lorentz
transformations, Einstein’s velocity addition formula |
Pages 487-500 of the textbook |
24 |
May 20 |
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 |
Pages 502-504 of the textbook |
Midterm Exam 3 |
May 22 |
|
|
25 |
May 25 |
Causal structure of Minkowski spacetime, 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 504-519 & 542-543 of the textbook |
26 |
May 27 |
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, the 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.