• Electrodynamics

    Dear students of Electrodynamics I

    This course will go over the first "unified field theory" in Physics, i.e., Classical Electrodynamics. The four Maxwell Equations not only managed to describe all electromagnetic phenomena, but also pointed to new applications and discoveries. But you have learned all that in your undergraduate courses on Electromagnetism.

    In this graduate course we will take advantage of the range of mathematical tools and acquired knowledge from related areas of Physics, to go deeper into the properties of electric and magnetic fields, boundary conditions, the dynamics of electromagnetic radiation, the interaction with matter, and so on.

    The basic textbook is, of course J. D. Jackson's "Classical Electrodynamics", which you can find almost anywhere. Other useful references are Griffith's "Introduction to Electrodynamics" (which you should consult if at any point you feel unsure about your background), as well as Greiner's "Classical Electrodynamics" and Zangwill's "Modern Electrodynamics". Another text which is sometimes helpful is Blandford & Thorne, "Applications of Classical Physics" (


    Below is a summary of the topics which we will try to cover during this course, over approximately 20 classes:

    Part 1: Electrostatics (~ 4-5 classes)

    1. Poisson and Laplace Equations
    2. Maxwell Equations
    3. Boundary conditions
    4. Conductors
    5. Advanced methods: Green’s functions; the method of images; separation of variables; multipole expansion

    Part 2: Dielectric materials, Magnetostactics & Magnetism in matter (~3 classes)

    1. Electric fields in matter
    2. Boundary conditions in matter
    3. Magnetostactics
    4. Applications of Ampère’s Law
    5. Magnetic fields in matter

    Part 3: Electrodynamics (~4 classes)

    1. Ohm’s Law, Faraday’s Law and Lenz’s Law
    2. Inductance
    3. Conservation equations
    4. Maxwell’s Equations revisited
    5. Electromagnetic radiation: emission & polarization

    Part 4: Electromagnetic waves (~6 classes)

    1. Gauge transformations
    2. Electromagnetic waves
    3. Wave mechanics
    4. Waves in vacuum
    5. Energy & momentum
    6. Relativity
    7. Relativistic Electrodynamics


    We will have two exams: a mid-term and a final exam. Your final grade will be based 40% on the mid-term, and 60% on the final exam.

    Both exams will be presential (there will be no online exams). The dates are:
    • P1: 03/05/2022
    • P2: 14/06/2022

    Videos of classes (2021):
    You can watch videos of the classes that were taught (online) in 2021 here:

    • Listas de exercícios

      As listas são idênticas às da disciplina de 2021. Ignore as datas de entrega, este ano (2022) as listas não serão cobradas.

      (ATENÇÃO: ignore as informações sobre a monitora da disciplina em 2021 que aparecem nos PDFs das listas -- ela não faz parte da equipe da disciplina neste ano.)

      1. Lista 1:

        Solução da Lista 1:

      2. Lista 2:

        Solução da Lista 2:

      3. Lista 3:

        Solução da Lista 3:

      4. Lista 4:

        Solução da Lista 4:

      5. Lista 5:

    • Notas (P1 e P2)

      Abaixo a tabela com as notas da P1 e da P2. As notas das Subs correspondentes já foram inseridas.

      (Notem que eu apliquei uma "renormalização" nas médias finais na hora de mapear nos conceitos A, B, C e R.)