Phys/Elec 312: Advanced Electromagnetism
Fall 2019
Topics Covered in Lectures
|
Lecture Number |
Date |
Content |
Corresponding Reading material |
|
1 |
Sep. 16 |
Coulomb’s law, electric field of one or
more point charges, electric field of a continuous distribution of charges,
flux of the electric field of a point charge, a collection of point charges,
and a continuous distribution of charges through a closed surface, the Gauss
law, vanishing of the curl of the electric field for a static charges medium
and the electric potential, formulation of electrostatics in terms of the
Poisson and Laplace’s equations |
Pages 59-86 of
the textbook (Griffith’s Introduction to Electrodynamics, 4th
Edition) |
|
2 |
Sep. 18 |
Electric potential for a dipole, multipole expansion,
dielectrics and their polarization due to an external electric field, the
surface and volume bound charge densities, statistical mechanical approach
for quantifying the electric field inside a dielectric |
Pages 154-156
& 172-180 of the textbook |
|
3 |
Sep. 23 |
Electric field of a homogeneous polarized sphere, average
electric field on sphere due to an arbitrary charge distribution, the
electric potential in a dielectric |
Pages 180-181 of
the textbook |
|
4 |
Sep. 25 |
Gauss’s law in a dielectric, isotropic linear dielectric
media, electric susceptibility and permittivity, energy in a dielectric |
Pages 181-202 of
the textbook |
|
5 |
Oct. 02 |
Lorentz force, current and current density, continuity
equation, Biot-Savart’s law |
Pages 211-231 of
the textbook |
|
6 |
Oct. 03 |
Divergence and curl of the magnetic field, Ampere’s law,
vector potential and gauge transformation, the Coulomb gauge, and vector
potential for a current density, boundary conditions for the vector
potential, multipole expansion for the vector potential of current loop |
Pages 231-254 of
the textbook |
|
7 |
Oct. 07 |
Magnetic dipole moment of current loop and its vector
potential, volume and surface bound currents, polarization of a dielectric due
to a magnetic field, magnetization, magnetic induction and Ampere’s law in a
dielectric |
Pages 255-287 of
the textbook |
|
8 |
Oct. 09 |
Energy of an electric (magnetic) dipole in an electric
(magnetic) field, Linear and nonlinear magnetic material, magnetic susceptibility
and permeability, Ohm’s law |
Pages 287-305 of
the textbook |
|
Quiz 1 |
Oct. 10 |
|
|
|
9 |
Oct. 14 |
Electromotive force, Faraday’s law, Equations for EM fields
before Maxwell, Maxwell’s equations in vacuum, Polarization current and Maxwell’s
equations in vacuum in matter |
Pages 307-325
& 336-348 of the textbook |
|
10 |
Oct. 16 |
Energy of a magnetic field, continuity equation for charge
and the local charge conservation; Poynting
theorem, local conservation of EM energy, and the corresponding continuity
equation |
Pages 213-216
of Jackson’s Classical Electrodynamics, 2nd Edition & Pages 360-364 of
the textbook |
|
11 |
Oct. 23 |
Maxwell’s stress tensor, local conservation of momentum and
angular momentum |
Pages 364-377 of
the textbook |
|
12 |
Oct. 30 |
Vibrating string, d’Alembert’s
solution, solution using Fourier transform, sinusoidal waves and their
complex wave functions, setup for scattering of a wave due to a jump in the
mass density of the string |
Pages 387-394 of
the textbook |
|
Quiz 2 |
Oct. 31 |
|
|
|
13 |
Nov. 04 |
Scattering due to a
jump in the mass density of a vibrating string, transverse versus
longitudinal waves, polarization; EM waves: Wave equation for EM fields in
vacuum, monochromatic plane waves, wave vector, and polarization, energy
density of a plane wave |
Pages 395-403 of
the textbook |
|
14 |
Nov. 06 |
Poynting vector, intensity, momentum density, and radiation
pressure of a plane wave, plane waves propagating in an isotropic and
homogeneous linear medium, scattering from a planar interface separating a
pair of dielectric media, Snell’s law |
Pages 403-412 of
the textbook |
|
15 |
Nov. 07 |
Fresnel’s equations and
Brewster’s angle, the reflection and transmission coefficients for TM waves,
EM wave propagation in a conductor |
Pages 413-420 of
the textbook |
|
16 |
Nov. 11 |
Reflection of a normally
incident plane wave from a conducting surface, Dispersion: Complex
permittivity, absorption and gain coefficients, Cauchy’s formula |
Pages 420-429 of
the textbook |
|
17 |
Nov. 13 |
Wave propagation in a
straight wave guide, Helmholtz equation, TE and TM modes, construction of the
TE modes of a rectangular wave guide |
Pages 430-435 of
the textbook |
|
18 |
Nov. 18 |
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 |
|
19 |
Nov. 20 |
Retarded and advanced
potentials, Jefimenko’s equations, the retarded (Lienard-Wiechart) potentials for a moving point charge |
Pages 561-572 of
the textbook |
|
Midterm
Exam |
|
|
|
|
20 |
Nov. 25 |
Derivation of the formulas
for the electric and magnetic fields of a moving point charge. |
Pages 573-577 of
the textbook |
|
21 |
Nov. 27 |
Radiation due to dynamical
charge distributions, radiation by an oscillating electric dipole. |
Pages 442-449 of
the textbook |
|
22 |
Dec. 02 |
Radiation by an arbitrary
dynamical charge distribution, Larmor’s formula for
power radiated by an accelerating charged particle |
Pages 453-457 of
the textbook |
|
23 |
Dec. 04 |
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: Relativity of the simultaneity,
time dilation, and Lorentz contraction. |
Pages 479-492 of
the textbook |
|
24 |
Dec. 09 |
Further discussion of
Lorentz contraction, Galilean transformations, Lorentz transformations, the
derivation of time dilation and Lorentz contraction from Lorentz
transformations, Einstein’s velocity addition rule |
Pages 492-500 of
the textbook |
|
25 |
Dec. 11 |
Minkowski space, Minkowski inner
product and metric, light cones and the causal structure of Minkowski space, proper time, proper velocity, proper
momentum, and energy of a relativistic free particle |
Pages 502-514 of
the textbook |
|
Quiz 3 |
Dec. 12 |
|
|
|
26 |
Dec. 16 |
Relativistic Newton’s equation, relativistic conservation
of momentum and energy, on possibility of zero-mass particles, the mass to
energy conversion in a decay process and its time-reversal; Relativistic
invariance of electrodynamics: Current 4-vector, invariance of continuity
equation and local conservation of electric charge, relativistic invariance
of d’Alembertian. |
Pages 514-519
& 542-543 of the textbook |
|
27 |
Dec. 18 |
Contravariant and covariant 4-vector potentials, relativistic
invariance of the Lorentz gauge condition, gauge transformations of the
4-vector potentials, covariant and contravariant electromagnetic field tensors,
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.