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, 4^th 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
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
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
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
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
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.