This course deals with Electrostatics, Magnetostatics and Maxwell’s equations.
Table of Contents
Resources
Two excellent (and free) books which cover these topics are
Classical Electromagnetism (by Richard Fitzpatrick, Professor of Physics at The University of Texas at Austin. Professor Fitzpatrick made these lectures available to the public via the website linked above.)
and
Electromagnetism (by David Tong, Professor at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. Professor Tong made these lectures available to the public via the website linked above. The author’s copyright stipulates: “Lecture notes copyright © 2015 David Tong unless otherwise credited. Permission is granted to copy and distribute freely, so long as proper attribution is given, no alterations are made, and no monetary profit is gained.”)
Students should also visit and explore Professor Tong’s Lectures on Electromagnetism website.
Weekly Plan
The table below includes a breakdown of the topics covered in each week of the course and links to the corresponding material in the websites by Prof. Fitzpatrick (RF lectures) and Prof. Tong (DT lectures)
| Week | Topic | RF lectures | DT lectures |
| 1 | Vector Calculus | – | Div, Grad and Curl |
| 2 | Maxwell’s equations | Ch 1 Maxwell’s Equations | Ch 1 Introduction |
| 3 to 5 | Electrostatics | Ch 2 Electrostatic Fields | Ch 2 Electrostatics |
| 6 to 8 | Magnetostatics | Ch 5 Magnetostatics Fields | Ch 3 Magnetostatics |
| 9 and 10 | Electric Fields in Matter | Ch 4 Electrostatics in Dielectric Media | Ch 7 Electromagnetism in Matter |
| 11 and 12 | Magnetic Fields in Matter | Ch 6 Magnetostatics in Magnetic Media | Ch 7 Electromagnetism in Matter |
| 13 and 14 | Electrodynamics | Ch 4 Electrodynamics |
The 15th (and last) week will be devoted to reviewing material and to the final exam.
Class notes
Here you can find links to some of the lecture notes used in class. The links and the notes are added, edited, and updated during the semester. (The class notes are written and edited by Andrea Ferroglia. The notes are licensed under CC BY NC.)
Vectors
- Vectors (review: components, scalar product, vector product)
- Differential vector calculus
- Integral vector calculus
- Curvilinear coordinates
- Two important identities
- Dirac delta function
Maxwell’s Equations
- Charges and currents
- Maxwell’s equations in vacuum
- Potential and gauge transformations
- Maxwell’s equations in integral form
- B and E at a boundary between two media
- Poynting vector
- Electric and magnetic fields in matter
Electrostatics
- Coulomb’s law
- Field lines
- Electrostatic energy
- Symmetric problems
- Conductors
- Capacitors
- Boundary value problems
- Method of images
- Method of images: grounded conducting sphere
- Method of images: charged sphere
- Electric dipoles
- The force between two dipoles
- Image dipole: a grounded sphere in a constant electric field
- Multipole expansion
- Legendre polynomials
- Monopoles, dipoles, quadrupoles
- Separation of variables: simple 2D example
- Completeness and orthogonality
- Fourier series and integral
- Separation of variables: 3D cartesian coordinates
- Separation of variables: Spherical coordinates with azimuthal symmetry
- Problems with azimuthal symmetry
Magnetostatics
- Magnetostatics – introduction
- Ampere’s Law
- Biot-Savart Law
- Magnetic dipole
- Dipole moment for a generic current
- Force between currents
- Force on a magnetic dipole
- Torque on a magnetic dipole
Electric fields in Matter
- Polarization in matter
- Polarized sphere
- Electric displacement D
- Linear dielectrics
- Boundary problem in dielectrics: method of images
- Dielectric sphere in an external field
Magnetic fields in Matter
- Magnetism in matter
- Magnetization
- The field H
- Magnetic permeability
- Ferromagnets
- Methods for boundary value problems involving H
- Uniformly magnetized sphere
