| Day and Date | Lecture Content and Homework Assignment |
|---|---|
| Fri. Aug. 20, 2010 |
Lecture: Random walk through undergraduate work, including vector calculus. Homework (HW #1: due 8/27): Jackson 1.1. |
| Mon. Aug. 23, 2010 |
Lecture: Quiz. Homework (HW #1: due 8/27): Jackson 1.2. |
| Wed. Aug. 25, 2010 |
Lecture: Coulomb's Law, the Electric Field, Gauss's Law. Homework (HW #1: due 8/27): Jackson 1.3. |
| Fri. Aug. 27, 2010 |
Lecture: HW problems. Homework: None. |
| Mon. Aug. 30, 2010 |
Lecture: The ELectric Potential. Curl and Divergence of E, Poisson
Equation. Surface Dipole Moment Density. Green's Theorem. Homework (HW #2: due 9/10): Jackson 1.11. |
| Wed. Sep. 1, 2010 |
Lecture: Solutions of the Poisson Equation: General properties including uniqueness. Homework (HW #2: due 9/10): This problem. |
| Fri. Sep. 3, 2010 |
Lecture: Solving Poisson's equation using Green's functions.
Energy in a configuration of charges. Energy Density in electric fields. Homework (HW #2: due 9/10): Jackson 1.14. |
| Wed. Sep. 8, 2010 |
Lecture: Significance of 1/2 in many electrostatic Energy
expressions. Capacitance. Action Principle and the Euler-Lagrange equations. Obtaining the Poisson equation from the Lagrangian density for Electrostatics. Homework (HW #3: due 9/17): Jackson 1.17. |
| Fri. Sep. 10, 2010 |
Lecture: The Method of Images: Charge near a conducting plane.
Connection with Green's Function Method. Homework (HW #3: due 9/17): Jackson 2.1. |
| Mon. Sep. 13, 2010 |
Lecture: The Method of Images: Charge near a conducting sphere, near a
charged sphere and near a sphere at a fixed non-zero potential.
Connection with Green's Function Method. Homework (HW #4: due 9/24): Jackson 2.2. |
| Wed. Sep. 15, 2010 |
Lecture: Conducting sphere immersed in a uniform Electric Field.
Potential due to a split sphere: hemispheres at +V and -V. Homework (HW #4: due 9/24): Jackson 2.9. |
| Fri. Sep. 17, 2010 |
Lecture: Potential due to a split sphere, continued. A short quiz:
Obtain the Fourier expansions of given periodic functions using
the usual sine / cosine Fourier series and using Legendre
polynomials. Discussion of the quiz. Homework (HW #4: due 9/24): Jackson 2.11. |
| Mon. Sep. 20, 2010 |
Lecture: Orthogonal Functions expansion method: Cartesian
coordinates. (3-D). Homework (HW #5: due 10/1): This problem. |
| Wed. Sep. 22, 2010 |
Lecture: Orthogonal Functions expansion method: Polar coordinates
(2-D), and fields near a sharp 2-D corner. Spherical polar coordinates
(3-D). Homework (HW #5: due 10/1): Jackson 2.26. |
| Fri. Sep. 24, 2010 |
Lecture: General solution for the case of spherical coordinates.
Spherical harmonics. Potential for the case of azimuthal symmetry. Homework (HW #5: due 10/1): Jackson 3.3. |
| Mon. Sep. 27, 2010 |
Lecture: Expansion of inverse distance in terms of Legendre
Polynomials. Examples of boundary value problem solutions for the case
of spherical coordinates. Homework (HW #6: due 10/8): Jackson 3.6. |
| Wed. Sep. 29, 2010 |
Lecture: Grounded spherical surface with one wedge at potential V (A
to C problem). Mean Value Theorem. Solution of the Laplace Equation in
Cylindrical coordinates. Homework (HW #6: due 10/8): Griffiths 3.37. |
| Fri. Oct. 1, 2010 |
Lecture: Solution of the Laplace Equation in Cylindrical coordinates. Homework (HW #6: due 10/8): This problem. |
| Mon. Oct. 4, 2010 |
Test #1 on Jackson Chapter 1, Chapter 2, and Chapter 3 up to and including section 3.6. Homework (HW #7: due 10/13): None. |
| Wed. Oct. 6, 2010 |
Lecture: Multipole expansion of the electric potential. Homework (HW #7: due 10/13): Jackson 4.1. |
| Fri. Oct. 8, 2010 |
Lecture: Electric field due to a dipole; integral of the electric field
in a spherical volume. Homework (HW #7: due 10/13): Griffiths 4.29. |
| Mon. Oct. 11, 2010 |
Lecture: Energy of a charge distribution in an external
field. Dielectrics and Polarization. Bound charges. Boundary
conditions for dielectrics. Homework (HW #8: due 10/22): Jackson 4.6. |
| Wed. Oct. 13, 2010 |
Lecture: Models of dielectric polarizability and connection to susceptibility. Energy density in dielectrics. Homework (HW #8: due 10/22): Jackson 4.12. |
| Mon. Oct. 18, 2010 |
Lecture: Two problems in dielectrics: (A) Image charge with planar dielectric boundary. (B) Dielectric sphere immersed in a uniform electric field. Homework (HW #9: due 10/29): Jackson 4.9. |
| Wed. Oct. 20, 2010 |
Lecture: Magnetostatics: the Laws of Biot & Savart and of
Lorentz. Ampere's Laws. Maxwell equations for magnetostatics. Gauge
freedom and gauge invariance. Homework (HW #9: due 10/29): Jackson 5.6. |
| Fri. Oct. 22, 2010 |
Lecture: Force on one current-carrying loop due to another.
Multipole expansion of vector potential. Homework (HW #9: due 10/29): Jackson 5.10. |
| Mon. Oct. 25, 2010 |
Lecture: Field of a magnetic dipole. Integral of B field in a
spherical volume. Homework (HW #10: due 11/5): Jackson 5.7. |
| Wed. Oct. 27, 2010 |
Lecture: Magnetic moment of a particle. Force and torque on a current
distribution placed in a magnetic field. Homework (HW #10: due 11/5): Jackson 5.11. |
| Fri. Oct. 29, 2010 |
Lecture: Magnetic materials. Vector potential due to
magnetization. Boundary conditions on magnetic fields. Homework (HW #10: due 11/5): Griffiths 6.13. |
| Mon. Nov. 1, 2010 |
Lecture: Solving magnetostatic problems using vector and scalar
magnetic potentials. Case of a uniformly magnetized sphere using a
scalar potential. Homework (HW #11: due 11/12): Jackson 5.19. |
| Wed. Nov. 3, 2010 |
Lecture: Case of a uniformly magnetized sphere using a vector
potential. Simplifications at the boundary of a high-permeability
material: the field is normal to the interface and the boundary is an
equipotential for the scalar potential. Homework (HW #11: due 11/12): Jackson 5.31. |
| Fri. Nov. 5, 2010 |
Quiz: A simple problem based on section 4.4 and using multipole concepts. Homework (HW #11: due 11/12): Jackson 4.10. |
| Mon. Nov. 8, 2010 |
Test #2 on Jackson Chapter 3 from section 3.7 onwards, Chapter 4, and
Chapter 5 up to and including section 5.8. Homework (HW #12: due 11/19): None. |
| Wed. Nov. 10, 2010 |
Lecture: Faraday's law of Induction. Lenz's law. Modification of
Maxwell's curl of E equation. Lorentz Force Law. Mutual and Self
inductance. Energy dissipation in a conductor. Homework (HW #12: due 11/19): Jackson 5.30. |
| Fri. Nov. 12, 2010 |
Lecture: Energy density in a Magnetic Field. Maxwell's modification of
Ampere's Law. The Maxwell equations of Electrodynamics. Gauge
Freedom. Wave equations for the scalar and vector potential and
exploiting the gauge freedom to decouple these equations. Homework (HW #12: due 11/19): Jackson 5.22. |
| Mon. Nov. 15, 2010 |
Lecture: Solution by Green functions of the equations of
electrodynamics for the potentials: part 1. Homework (HW #13: due 11/29): Jackson 6.1. |
| Wed. Nov. 17, 2010 |
Lecture: Solution by Green functions of the wave equation for the
potentials: part 2. Discussion of retarded and advanced
potentials. Time machine and travel back in time to understand the
solution for the potentials. Homework (HW #13: due 11/29): This problem. |
| Fri. Nov. 19, 2010 |
Lecture: Two examples of retarded potentials and the fields from them:
Homework (HW #13: due 11/29): Jackson 6.2. |
| Mon. Nov. 22, 2010 |
Lecture: The Poynting vector and energy flow. The electromagnetic wave
equation and plane waves. Complex values for k. Homework (HW #14: due 12/3): (a) Justify J⋅E as being the rate of Ohmic heating per unit volume. (b) Consider that the electromagnetic fields are actually real and not complex. Obtain expressions for S and u when the fields are "complex", i.e., obtain / justify the complex equations preceding Jackson's equations (7.13) and (7.14). |
| Mon. Nov. 29, 2010 |
Lecture: Energy density in the magnetic field of an electromagnetic
wave. Polarization of electromagnetic waves. The Maxwell Stress Tensor. Homework (HW #14: due 12/3): Griffiths 8.4. |
| Wed. Dec. 1, 2010 |
Lecture: Reflection and transmission of electromagnetic waves at a
boundary between two media. Homework (HW #14: due 12/3): Jackson 7.2. |
| Fri. Dec. 3, 2010 |
Lecture: Discussion of Brewster angle, total internal reflection. Course Review. Homework: None. |
| Thu. Dec. 9, 2010 9:00 AM - 12:00 noon | FINAL EXAM: Covers ALL material! |