1
Vector and tensor transformations; pseudo-vectors. Brief review of vector identities.
Griffiths, pp. 10-12.
2
Vector derivatives: gradient, divergence, curl. Product rules, second derivatives.
Griffiths, pp. 13-24.
3
Integral theorems: gradient, Gauss's, Stokes's.
Griffiths, pp. 24-38.
4
Polar coordinates: volume, area and length differentials; gradient, divergence and curl in polar coordinates; coordinate transformations.
Griffiths, pp. 38-45; Appendix A.
5
Dirac delta function. Helmholtz theorem; scalar and vector potentials.
Griffiths, pp. 45-54; Appendix B.
6
Coulomb’s Law, units. E as a vector field. E from point charges; superposition. Example of calculation of field from Coulomb's law. Lines of E.
Griffiths, pp. 58-69.
7
Flux of E , divergence of E and Gauss' Law. Examples of field calculations using Coulomb's and Gauss' laws.
Griffiths, pp. 69-74
8
More Gauss' Law examples. Curl of E (= 0 in electrostatics).
Griffiths, pp. 76-77.
9
Electric (scalar) potential V. Arbitrariness of reference potential. Superposition. Poisson's and Laplace's equation. Example calculations of potential.
Griffiths, pp. 77-86;
10
Boundary conditions; summary of calculation paths: Purcell's triangle.
Griffiths, pp. 87-93
11
Work and energy; relation to F and V; non-superposition. Examples.
Griffiths, pp. 93-96
12
Conductors in electrostatics. Induced charge, force between charges and conductors. Examples.
Griffiths, pp. 96-103.
13
Capacitors. Examples of parallel plates, concentric spheres, one sphere.
Reading: Griffiths, pp. 103-106.
14
Calculation of V from Laplace's equation: introduction to boundary value problems in physics.
Griffiths, pp. 110-120.
15
Properties of solutions to Laplace's equation. Averages, lack of local extrema, uniqueness of solutions.
Griffiths, pp. 110-120 (again).
16
Calculation of V by method of images. Induced charge on conductors; example of point charge and conducting sphere.
Griffiths, pp. 121-126.
Midterm examination on all material covered to date.
17
Solution of Laplace's equation by separation of variables. Example of semi-infinite slot: harmonic solutions, Fourier coefficients.
Griffiths, pp. 127-136.
18
Solution of Laplace's equation by separation of variables, in spherical coordinates; Legendre polynomials. Example of conducting sphere in uniform applied electric field.
Griffiths, pp. 137-150.
19
Multipole expansions of the potential; potential and field from an electric dipole. Polarizability, Dielectrics and electric susceptibility.
Griffiths, pp. 151-185
20
Linear Dielectrics
Griffiths, pp. 185 - 208
21
Begin magnetostatics: Lorentz force law; cyclotron motion; force on a steady current. Current density, continuity equation.
Griffiths, pp. 210-223.
22
Magnetic fields from Biot-Savart Law: force between two currents; field from a circular loop. Divergence and curl of B, Ampere's Law
Griffiths, pp. 234-242.
23
Vector potential A. Example of calculation of A , then B, from spinning, charged spherical shell.
Griffiths, pp. 242-255.
24
Magnetic fields in matter; Magnetization vector field M; bound currents; magnetic vector field H.
Griffiths, pp. 266-279.
25
Calculation of B and H in linear media. Magnetic susceptibility and permeability. Dia- and para-magnetism. Boundary conditions.
Griffiths, pp. 279-287
26
Electrodynamics. Ohm's law, simple treatment of collisions, resistance. EMF and magnetic flux
Griffiths, pp. 296-311.
27
Electromagnetic Induction; Faraday's Law
Griffiths, pp. 312-328
28
More on Faraday's Law, Inductance, and energy in magnetic fields
Griffiths, pp. 321-332
29
Introduction to Maxwell's equations
Griffiths, pp. 332-340
Final examination, covering all material introduced during the course.