Date

Subject

Reading

1

4 September

Vector and tensor transformations; pseudo-vectors. Brief review of vector identities.

Griffiths, pp. 10-12.

2

6 September

Vector derivatives: gradient, divergence, curl. Product rules, second derivatives. Griffiths, pp. 13-24; Purcell, pp. 46-48, 56-64, 68-79.

3

9 September

Integral theorems: gradient, Gauss's, Stokes's. Griffiths, pp. 24-38.

4

11 September

Polar coordinates: volume, area and length differentials; gradient, divergence and curl in polar coordinates; coordinate transformations. Homework 1 due; homework 2 assigned. Griffiths, pp. 38-45; Appendix A.

5

13 September

Dirac delta function. Helmholtz theorem; scalar and vector potentials. Griffiths, pp. 45-54; Appendix B.

6

16 September

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

18 September

Flux of E , divergence of E and Gauss' Law. Examples of field calculations using Coulomb's and Gauss' laws. Griffiths, pp. 69-74; Purcell, pp. 22-31.

8

20 September

More Gauss' Law examples. Curl of E (= 0 in electrostatics). Griffiths, pp. 76-77.

9

23 September

Electric (scalar) potential V. Arbitrariness of reference potential. Superposition. Poisson's and Laplace's equation. Example calculations of potential. Griffiths, pp. 77-86; Purcell, 42-46, 48-56.

10

25 September

Boundary conditions; summary of calculation paths: Purcell's triangle. Homework 3 due; homework 4 assigned. Griffiths, pp. 87-93; Purcell, pp. 64-67.

11

27 September

Work and energy; relation to F and V; nonsuperposition. Examples. Griffiths, pp. 93-96; Purcell, pp. 31-33.

12

30 September

Conductors in electrostatics. Induced charge, force between charges and conductors. Examples. Griffiths, pp. 96-103.

13

2 October

Capacitors. Examples of parallel plates, concentric spheres, one sphere. Homework 4 due; homework 5 assigned. Reading: Griffiths, pp. 103-106.

14

4 October

Calculation of V from Laplace's equation: introduction to boundary value problems in physics. Example to show how it works, first. Griffiths, pp. 110-120.

15

9 October

Properties of solutions to Laplace's equation. Averages, lack of local extrema, uniqueness of solutions. Instability of electrostatic mechanical equilibrium. Homework 5 due; homework 6 assigned.

 Griffiths, pp. 110-120 (again).

16

11 October

Calculation of V by method of images. Induced charge on conductors; example of point charge and conducting sphere.

Griffiths, pp. 121-126.

17

14 October

Solution of Laplace's equation by separation of variables. Example of semi-infinite slot: harmonic solutions, Fourier coefficients.

 Griffiths, pp. 127-136.

18

16 October

Solution of Laplace's equation by separation of variables, in spherical coordinates; Legendre polynomials. Example of conducting sphere in uniform applied electric field. Homework 6 due.

 Griffiths, pp. 137-144.

19

18 October

Complete boundary-value examples.

 Griffiths, pp. 127-144 (again).
  18 October, 3:25-4:40 PM Midterm examination on all material covered to date.

20

21 October

Multipole expansions of the potential; potential and field from an electric dipole.

 Griffiths, pp. 146-154.

21

23 October

Polarizability; induced dipoles; torque on electric dipole in uniform electric field. Polarization vector field. Homework 7 assigned.

 Griffiths, pp. 160-166.

22

25 October

Bound charge. Electric fields from polarized media. The electric displacement vector field.

 Griffiths, pp. 166-179.

23

28 October

Dielectrics and electric susceptibility. Some calculations of E and V for linear dielectrics.

Griffiths, pp. 179-193.

24

30 October

Forces and energy in dielectrics; capacitor oil-pump example. Homework 7 due; homework 8 assigned. Griffiths, pp. 193-196.

25

1 November

Begin magnetostatics: Lorentz force law; cyclotron motion; force on a steady current. Current density, continuity equation.

Griffiths, pp. 202-214.

26

4 November

Magnetic fields from Biot-Savart Law: force between two currents; field from a circular loop.

Griffiths, pp. 215-220.

27

6 November

Divergence and curl of B, derivation of Ampere's Law. Homework 8 due; homework 9 assigned.

 Griffiths, pp. 221-224.
28 8 November

Calculation of B from Ampere's Law: solenoid, toroid.

 Griffiths, pp. 225-232.
29 11 November

Comparison of magnetostatics and electrostatics. Vector potential A. Example of calculation of A , then B, from spinning, charged spherical shell.

Griffiths, pp. 232-238.
30 13 November

Boundary conditions; summary of calculation paths, using Purcell's other triangle. Homework 9 due; homework 10 assigned.

 Griffiths, pp. 240-242.
31 15 November

Magnetic multipoles; calculation of magnetic dipole moment from current loop; torque on the loop; comparison between electric and magnetic dipoles.

Griffiths, pp. 242-246.
32 18 November

Magnetization vector field M; bound currents; magnetic vector field H. Dia- and para-magnetism. Boundary conditions.

Griffiths, pp. 255-274.
33 20 November

Calculation of B and H in linear media. Magnetic susceptibility and permeability. [Leave out ferromagnetism. pp. 278-282] Homework 10 due; homework 11 assigned.

 Griffiths, pp. 274-277.
34 22 November

Begin electrodynamics. Ohm's law, simple treatment of collisions, resistance. Examples.

 Griffiths, pp. 285-290.
35 25 November

EMF and magnetic flux; some examples; Faraday's Law.

 Griffiths, pp. 292-304.
36 27 November

Examples of use of Faraday's Law; magneto-quasistatics. Homework 11 due.

 Griffiths, pp. 305-309.
37 2 December

Inductance, transformers. Energy in magnetic fields.

 Griffiths, pp. 310-320.
38 4 December

Kirchhoff's rules, resistor networks. Homework 12 assigned.

Purcell, pp. 148-159.
39 6 December

Time-dependent currents: RC and RL circuits.

 Purcell, pp. 159-161, 282-286.
40 9 December

AC circuits; series LRC circuit, resonance, Q.

 Purcell, pp. 298-310.
41 11 December

AC networks; impedance and admittance. Homework 12 due.

 Purcell, pp. 310-318.

 

21 December, 4-7 PM

Final examination, covering all material introduced during the course.