8.022: Electricity & Magnetism

Over the years of teaching 8.022, I've developed a fairly complete set of lecture notes on electricity and magnetism. Some people have found them to be useful, so I'm posting them here. Feel free to use them for anything, but make sure to leave all the header information in place [my name, the lecture number and topic, and the semester in which these particular notes were finalized (Spring 2005)].

These notes follow the schedule and syllabus of Spring 2005, and may not precisely sync up with the schedule of other semesters.

Finally, these notes are provided as is; I don't guarantee that they are free of typos or stupid mistakes. Please send me corrections via email; I'll post corrections when I have time.

1. Introduction: Coulomb's law, superposition, energy of a system of charges.

2. Electric field: Basic field concept, flux, Gauss's law.

3. More electrostatics: Energy in the field, potential. Some math: gradient and divergence; revisiting Gauss's law.

4. Divergence and curl: This lecture was described by at least one student as "all of 18.022 in a single lecture".

5. Conductors: Fields and potentials around conductors; the electrostatic uniqueness theorem.

6. Capacitance.

7. Current: Basic notions. Current density, current, continuity, Ohm's law.

8. Circuits: Basic notions. EMF and Kirchhoff's rules.

9. Variable currents: RC circuits, Thévenin equivalence.

10. Magnetic fields and forces: Basic properties of the magnetic field and the forces it exerts; special relativity not assumed. This deviates from Purcell's approach.

10a. Clarification to Lecture 10: One calculation in Lec 10 was rather confusing; these notes are my attempt to clear things up.

11. Special relativity 1: Time dilation, length contraction, Lorentz transformations, tranformation of velocity.

12. Special relativity 2: Forces and fields in special relativity. Equivalence of the electric and magnetic forces.

13. Return to magnetic fields.

14. Introduction to Induction: Faraday and Lenz.

15. Mutual and self inductance.

Notes on complex numbers. The only sane way to analyze AC circuits, in my not-so-humble opinion.

16. RL circuits, undriven RLC circuits: What we get when inductors and resistors are combined in circuits. Also introduces the use of complex numbers to analyze circuits.

17. AC circuits and impedance: Our first examination of alternating current circuits. Key things to learn here: life is a lot easier if we use complex numbers in our analysis; Ohm's law works perfectly for all circuit elements --- resistors, capacitors, inductors --- provided we use a quantity called "impedance" to relate voltage and current.

18. More on AC circuits: Power in AC circuits; resonance and filters.

19. Displacement current and Maxwell's equations: Here we finally put everything together and get the full set of "field equations" which describe electricity and magnetism.

20. Wave equation and radiation: Here we massage Maxwell's equations a bit and find a particularly interesting solution: Electromagnetic radiation.

21. Polarization and scattering: Some particularly interesting and important properties of radiation.

22. Energy and momentum in radiation: We examine how electromagnetic energy flows, deriving an extremely important quantity (the Poynting vector).

Note: The following two lectures were not part of the core 8.022 material when I lectured (particularly lecture 24!).

23. Magnetic fields and materials.

24. A (very) brief introduction to general relativity.