Physics 331: Electricity and Magnetism
James Cook's Physics 331: Electricity and Magnetism
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Lecture Plan and Notes:
I should post my handwritten Lecture Notes from Physics 331 of Fall 2025 here. Probably they're just ripped out of Griffiths, except when they're not.
- Lecture 1: Vectors and Calculus: index notation for calculus and vectors.
- Lecture 2: Coordinate Frames: from geometry and calculus.
- Lecture 3: Dirac Delta Device: special nature of Coulomb field, introduction of Dirac Delta in one and three dimensions.
- Lecture X: Curl and Divergence in Curvelinear Coordinates here I work through the Appendix in Griffiths where the formulas for curl and divergence in cylindrical or spherical coordinates are given (WARNING: I wrote this up for Calculus III and as such I used the bizarro math spherical notation )
- Lecture 4: Static Electric Field: Coulomb field, field lines and derivation of Gauss Law.
- Lecture 5: Gauss Law and Dirac Deltas: Gauss Law and basic spherical, cylindrical and planar examples, also we study how the Dirac Delta function plays into these examples.
- Lecture 6 7: From Electric Fields to Potentials: interconnection of E-field, potential and charge density. Calculational techniques, conservative vector field properties of E, boundary conditions for field and potential. Formulation of potential either from integration of density or from integration of known E-field, conductors. (this concludes Chapter 2 of Griffiths)
- Lecture 8: Uniqueness Theorem for Laplace's Equation I included the explicit application to the method of images. I merely include the most important example of the method of images and how it allows us to derive the induced charge on the conducting plane due to a single point charge above the plane.
- Lecture 9: Laplace's Equation in Spherical or Cartesian Coordinates (separation of variables and Fourier techniques)
- Lecture 10: Laplace Equation in Spherical or Cylindrical coordinates (ok, we didn't get very far into the cylindrical case)
- Lecture 11: Legendre Polynomial Solutions of Laplace's Equation
- Lecture 12: Multipole Expansion potentials and fields can be seen as superposition of poles at origin
- Lecture 13: Electrostatics in Matter concept of polarization, dipole moment, bound charge in insulators
- Lecture 14: Electric Displacement and Linear Dielectrics construction of D, susceptibility and permitivity in linear dielectrics, boundary values, nontrivial curl of polarization of bar electret
- Lecture 15: Crystals, Capacitors and Energy summary thoughts about end of Chapter 4 in on Electrostatics in matter.
- Lecture 16: Magnetic Fields: derivation of Ampere's Law from the Biot-Savart Law mathematical primer on Biot-Savart and how we derive Ampere's Law.
- Lecture 17: Magnetic Fields: discussion of current distributions, conservation of charge and the continuity equation, examples of common magnetic fields both from Biot-Savart and Ampere's Law probably this material belongs before Lecture 16, much of this is really material from Physics 132.
- Lecture 18: The Vector Potential: definition and non-uniqueness, we discuss why scalar magnetic potential cannot be globally defined
- Lecture 19: Magnetic Monopole and the Aharonov-Bohm effect: we derive the vector potential for the magnetic monopole and note the Dirac-String type divergence which must appear, physicality of vector potential shown via Aharonov-Bohm example.
- Lecture 20: Boundary Conditions and Magnetostatics in Matter: we study magnetic field and vector potential at boundary surface, spinning charged spherical shell example worked in detail, magnetization introduced and uniformly magnetized sphere seen to connect to spinning charged sphere.
- Lecture 21: Magnetostatics in Matter: uniformly magnetized sphere revisited, bound currents derived, auxillary field H discussed and applied. Diagmagnetism, Paramagnetism and Ferromagnetism contrasted (not much said on Ferromagnetism, my apologies)
- Lecture 22: EMF and Faraday's Law: discussion of motional EMF and other EMFs given, then connection to Faraday's Law through Griffith's "Universal Flux Rule". Maxwell's Law known as Faraday's Law introduced. Novel calculation of induced electric field via magneto static analogy shown. Quasistatic approximation introduced and cautionary example given.
- Lecture 23: mutual inductance, Maxwell's correction term:
- Lecture 24: Poynting vector and Poynting's Theorem:
- Lecture 25: Stress Energy Tensor: here we derive the force due to the electromagnetic field, it turns out we need an object called a "tensor" to capture the combined action of both the electric and magnetic fields.
- Lecture 26: conservation of momentum, energy and angular momentum: here we see how the Stress Energy tensor and Poynting vector describe energy and momentum in the electromagnetic field.
- Lecture 27: Wave Equation: derivation of wave equation from Maxwell's Equation in vacuo.
- Lecture 28: Complexified Wave Equation and Superposition: complexifying wave equation gives nice formalism to treat problems involving calculation of phase for superposition of waves of a common frequency, example of phasor method given.
- Lecture 29: Refraction derived from Electromagnetism: electromagnetic waves and complex notation, refraction derived from boundary conditions on electric and magnetic fields at interface
- Lecture 30: Electromagnetic Waves in Conductors: electromagnetic waves in conductors, attenuated wave equation, skin-depth.
- Lecture 31: Electromagnetic Waves in Cavities: electromagnetic waves in cavities, TEM modes, coaxial cable example.
- Lecture 32: Gauge Freedom and Retarded Potentials: potential formulation of electromagnetism, time-dependent vector potentials and Gauge choices, retarded time and the construction of retarded potentials, time-varying current example
- Lecture 33: Jefimenko's Equations and Lienard Wiechert Potentials for Point Charge: Jefimenko's Equations for E and B fields based on retarded source charge density and current, Lienard Wiechert retarded potentials for the point charge, constant velocity example.
- Lecture 34: E and B fields of point charge in arbitrary motion: electric and magnetic fields of point charge in arbtrary motion, retarded potential derivation of the radiation fields
- Lecture 35: Constant Velocity Fields, Thomson Kink Model: constant velocity point charge's electromagnetic fields, Thomson Kink Model qualitative radiation field picture)
- Lecture 36: Far Field Radiation: here I give a very abbreviated treatment of Chapter 11 of Griffiths. I discussed more in-lecture. My apologies we did not cover radiation-reaction.
- Lecture 37: Special Relativity: Lorentz Transformations for Minkowski Space, the Minkowski metric, invariant interval, contravariant and covariant 4-vectors, raising and lowering indices via the metric, Poincare group
- Lecture 38: 4-Vectors and Physics: Mechanics in space time, proper velocity, proper acceleration and forces, relativistic velocity, relativistic momentum, frame-invariant calculational techniques, conservation of energy and momentum, Compton Scattering.
- Lecture 39: Field Tensor: construction of field tensor from the 4-potential, components of field tensor and dual tensor, derivatives of field tensor and their connection to Maxwell's Equations, homogeneous Maxwell's equations from the dual tensor ala Griffiths, discussion of differential forms formulation of field tensor as 2-form, tensorial nature of field tensor given tensorial nature of 4-potential, transformation laws for fields.
- Lecture 40a: Classical Field Theory: introduction to variational calculus for field theories, derivation of Maxwell's Equations from variational principle ( would like to add pseudo-derivation of electromagnetism as a U(1) gauge theory from Ryder's QFT text, don't have it with me presently, but I should have notes somewhere from when I worked through it in graduate school )
Lecture 40b: Isospin and Quarks: this is a talk I gave in a Lie Algebra representation theory course at NCSU. In it I explain the concept of Isospin and how it led us to discover the quark content of nuclei. Ideally I will finish this lecture with a couple minutes about how Yang Mill's Theory generalized electromagnetism from the gauge group U(1) to arbtrary gauge group. The mathematics of this is the theory of connections on vector bundles paired. This has been known since about 1970.
Missions and Tests for Physics 331:
Solved Problems from 3rd ed. of Griffiths:
These solutions are mine from my undergraduate work at NCSU in the previous millennium.
Notes from my time at NCSU:
These are probably not helpful, I post them here for my amusement. These are based on the 3rd edition of Griffith's Introduction to Electrodynamics
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Last Modified: 11-28-2025