**ElectromagneticTheory 2014** Colorado Mesa *University*

*University*

*Textbook*:D. J. Griffiths, Introduction to Electrodynamics, 4th ed, Prentice Hall,2013

*Textbook*

Course description:

Mathematical tools: vector algebra, calculus in three dimensions; Electrostatics, Coulomb’s law, Gauss’ law; Work and energy in electrostatics, electric potential, Poisson’s equation, Laplace’s equation; Multipoles; Magnetic fields and forces, Biot-Savart law, Ampere’s law, magnetic vector potential; Induction, Faraday’s law; Maxwell’s equations; Electric fields in matter, polarization, dielectrics; Magnetic fields in matter.

**Electromagnetic Field Theory – Spring 2014**

For Lectures Notes, Homework solution

## Textbook:

- Zangwill – Modern Electrodynamics, Google Books
- Garg – Classical Electromagnetism in a Nutshell, Google Books
- J.D. Jackson – Classical Electrodynamics, 3rd Edition, Google Books
- H.C. Ohanian – Classical Electrodynamics, 2nd Edition, Google Books

**Topics: **Electrostatics of Dielectrics, Magnetostatics: Biot and Savart Law, Ampere’s Law, Vector Potential, Magnetic Moment, Boundary Value Problems in Magnetostatics, Maxwell Equations, Green Functions for Wave Equation, Poynting Vector, Maxwell, Stress Tensor , Electromagnetic Waves and their Propagation, Radiation, Multipole Expansion, Scattering and Diffraction, Optical Theorem, Special Relativity, Relativistic Charges in Electromagnetic Fields, Radiation by Moving Charges, Radiation Damping.

**Electromagnetic Theory I**

**Textbook**: *Classical Electrodynamics*, 3rd edition by J.D. Jackson

Lecture Notes Homework and Solution

- Lecture 1 – From Coulomb to Maxwell: charge, Coulombs law, the electric field, differential and integral form of Maxwell’s equations for electrostatics
- Lecture 2 – From Coulomb to Maxwell: Lorentz force, the magnetic field, current density, charge conservation and the definition of magnetostatics, Maxwell’s equations for magnetostatics, Faraday’s Law, Maxwell’s correction to Ampere’s Law, EM waves
- Lecture 3 – Systems of units, scalar and vector potentials, gauge invariance, Lorentz gauge, Coulomb gauge
- Lecture 4 – Longitudinal and transverse parts of a vector function, review Fourier transforms, physical meaning of the electrostatic potential, Green’s function, conductors in electrostatics
- Lecture 5 – Coulomb problem as a boundary value problem, electric field at a charged surface, Dirichlet vs Neumann boundary condition, examples, Green’s identities and uniqueness

Green’s functions, part II – Greens functions for Dirichlet and Neumann boundary conditions – we will not go over this in lecture.

- Lecture 6 – The image charge method for a charge in front of an infinite plane, and in front of a conducting sphere
- Lecture 7 – Separation of variables method in rectangular and polar coordinates
- Lecture 8 – Separation of variables method in spherical coordinates, Legendre polynomials

Green’s functions, part III – Eigenfunction expansion for the Greens function – we did not go over this in lecture, but it provides some of the theoretical basis for why the separation of variables method works

- Lecture 9 – Multipole expansion: monopole, dipole and quadrupole moments
- Lecture 10 – Multipole expansion continued, magnetostatics, magnetic dipole approximation
- Lecture 11 – Magnetostatic scalar potential, boundary conditions at a sheet current, examples
- Lecture 12 – Symmetry under parity transformations, Macroscopic Maxwell’s equations: dielectrics
- Lecture 13 – Macroscopic Maxwell’s equations: polarization density, electric dispacement field
**D**, magnetic materials, paramagnetism and diamagnetism, bound currents - Lecture 14 – Macroscopic Maxwell’s equations: magnetization density,
**H**field, bound surface current, conservation of bound charge, boundary conditions - Lecture 15 – Linear Materials: electric and magnetic susceptibilities, dielectric constant, magnetic permeability, atomic polarizability and the Clausius-Mossotti equation, boundary condition problems
- Lecture 16 – Point charge in a dielectric sphere, bar magnets, electromagnetism and conservation of energy
- Lecture 17 – Electromagnetic energy density, Poynting vector, conservation of momentum, Maxwell stress tensor, force on a conducting surface
- Lecture 18 – Capacitance matrix, inductance matrix, electromagnetic waves in a vacuum

Supplement – Force, torque, and interaction energy for electric and magnetic dipoles in an external field – we did not go over this in lecture.

- Lecture 19 – Energy and momentum in electromagntic waves, frequency dependent atomic polarizability, frequency dependent dielectric function
- Lecture 20 – Electromagnetic waves in a dielectric: transparent propagation, resonant absorption, total reflection
- Lecture 21 – Electromagnetic waves in conductors: frequency dependent conductivity, low frequency “good” conductors, skin depth, high frequencies, longitudinal modes and plasma oscillations
- Lecture 22 – Linear, circular and elliptical polarization, waves at interfaces, angles of incidence, reflection and transmission
- Lecture 23 – Snell’s law for transparent and dissipative media, total internal reflection, coefficient of reflection
- Lecture 24 -Total reflection, Brewster’s angle, Kramers-Kronig relation, Green’s function for the wave equation
- Lecture 25 – Lienard-Weichert potentials for a moving charged particle, potentials from a particle moving with constant velocity, radiation from a source oscillating with simple harmonic motion
- Lecture 26 – Electric dipole, magnetic dipole, and electric quadrupole radiation; fields, Poynting vector and radiated power
- Lecture 27 – Radiation from a general time dependent source, Larmor’s formula for radiation from an accelerating charge, special relativity, Lorentz transformation, 4-vectors
- Lecture 28 – Proper time, 4-velocity, 4-gradient, 4-current, 4-potential, field strength tensor and Maxwell’s equations
- Lecture 29 – Energy-momentum 4-vector, Lorentz force, relativistic Larmor’s formula

**ELECTROMAGNETIC THEORY II (Spring 2013)**

**Textbook:** Classical Electrodynamics (3rd Edition) by J. D. Jackson

**Lecture Notes, Homework Answers and Exam Solutions**

- Maxwell equations, plane vectors, polarization, Stokes parameters, Jones vector, reflection, refraction, Brewster’s angle, total internal reflection
- Complex permmitivity, resonant absorption, conductivity, plasma frequency
- Superposition of waves, group velocity, pulse spreading, dispersion, Kramers-Kronig relation
- Fields at the surface of an imperfect conductor, waveguide equations
- Rectangular waveguides, cutoff Frequency, resonant cavities, Q-factor
- Radiation, long-wavelength approximation, far-field waves, dipole radiation
- Linear antennas
- Long-wavelength scattering, polarization-dependent cross-sections, scattering by a small dielectric sphere, scattering matrix
- Scattering by a conducting sphere, atmospheric scattering
- Galilean relativity, ether, Einstein’s postulates
- Einstein’s principle of relativity, Lorentz transformations, Four-vectors
- Velocity addition in special relativity, relativistic momentum and energy
- Covariant geometry, covariant Maxwell’s equations

## electromagnetic waves

Introduction to Electromagnetics

**Text Book: **F.T. Ulaby, Fundamentals of Applied Electromagnetics, Prentice Hall 2009

*Lectures Video **The University of UTAH- Fall 2012*

**Course Material: **Introduction to electromagnetics. Fundamentals of wave propagation, transmission lines, impedance matching, electrostatics, magnetostatics, Maxwell’s equations, plane waves in free space, lossy media, and reflections from planar interfaces, wireless communication systems. Electromagnetic safety. Applications include wireless communication systems, high speed digital circuits, electromagnetic sensors, and bioelectromagnetics.

**Electromagnetic fields and energy**