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, 4^th 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.