All references to "Jackson" are to the third edition of our course text by Jackson.
| Day of week and Date | Lecture Content and Homework Assignment |
|---|---|
| Fri. Aug. 24, 2012 |
Lecture: Coulomb's Law, Gauss's Law, Dirac Delta functions. Homework #1: Prove all the theorems on the inside front cover and facing page of Jackson. |
| Mon. Aug. 27, 2012 |
Lecture: Potentials, path independence, work done in moving a charge
against an electric field. Potential due to a surface dipole moment density. Homework #2: Jackson 1.1. |
| Wed. Aug. 29, 2012 |
Lecture: Poisson Equation and its simple solution. Integral form of
the Poisson Equation, and the meaning of the terms therein. Uniqueness
of the solution. Homework #2: Jackson 1.5. |
| Fri. Aug. 31, 2012 |
Lecture: The Green function approach: the meaning of Green
functions. Green functions are not unique until you specify the
boundary conditions. Conditions on the Green Function needed to
obtain solutions to the Poisson equation for Dirichlet
and Neumann boundary conditions. Homework #2: Jackson 1.14. |
| Tue. Sep. 4, 2012 |
Lecture: Energy in a configuration of charges and in a continuous charge distribution.
Capacitance. Integral form using a variational principle. Homework #3: Jackson 1.17. |
| Wed. Sep. 5, 2012 |
Lecture: Discussion of Jackson Chapter 1 and problems therein. Homework #3: Jackson 1.15. |
| Fri. Sep. 7, 2012 |
Lecture: Outward pressure on a conducting surface. The method of
images applied to the simple problem of a point charge near a large,
grounded conducting plane. Homework #3: Jackson 1.6c, 1.19. |
| Mon. Sep. 10, 2012 |
Lecture: Test #1. Covers Chapter 1 of Jackson. Homework: None. |
| Wed. Sep. 12, 2012 |
Lecture: The method of images applied to a charge near a conducting
sphere which is (a) grounded or (b) has a given charge Q or (c) is at a given potential V0. Homework #4: Jackson 2.2. |
| Fri. Sep. 14, 2012 |
Lecture: Problem of a conducting sphere placed in a uniform electric
field solved using the method of images. Homework #4: Jackson 2.5. |
| Mon. Sep. 17, 2012 |
Lecture: Solution of the problem of a conducting sphere whose two
hemispheres are at potentials +V and -V using the Green function approach. Homework #5: Jackson 2.7. |
| Wed. Sep. 19, 2012 |
Lecture: Basis Functions. Generalized Fourier series and expansions. Fourier
Transforms. Homework #5: Consider the surface of a sphere which has been divided into an even number of segments, like the wedges in an orange. Consider a function which is +1 or -1 on alternate wedges. Expand this function in terms of the spherical harmonics. Try to evaluate all terms up to and including ℓ=3 for the case of just two segments. |
| Fri. Sep. 21, 2012 |
Lecture: The method of separation of variables for Cartesian
coordinates in 3 dimensions and
Cylindrical coordinates in two dimensions. Homework #5: Find the potential in a charge-free cuboidal volume where the cuboid sizes are 1, 2, and 3 m respectively in x, y, and z, and where the potential on the faces is zero except for the two z faces which are at 1V (z=0) and 2V (z=3m). |
| Mon. Sep. 24, 2012 |
Lecture: The Laplace equation in Cylindrical coordinates in two
dimensions, concluded: potential in region bounded by two intersecting
planes at the same potential. Solutions to the Laplace equation in Spherical
coordinates. The spherical harmonics. Homework #6: Jackson 3.2. |
| Wed. Sep. 26, 2012 |
Lecture: Properties of the spherical harmonics. Electrostatic
potential problems involving azimuthal symmetry. Expansion of the
inverse of the distance between two points. Homework #6: A dipole of moment p has orientation (θ', φ') at location xp. What is the potential due to this dipole at field point x? Use the methods of this lecture to solve the problem. What is the electric field due to this potential? Hints #1 Hints #2 |
| Fri. Sep. 28, 2012 |
Lecture: More on the spherical harmonics: Behavior under rotations.
The addition theorem. Laplace equation in cylindrical coordinates. Homework #6: Jackson 3.3. Hints |
| Mon. Oct. 1, 2012 |
Lecture: Preponed to Tue., Sep. 4. Homework #7: None. |
| Wed. Oct. 3, 2012 |
Test #2a. Covers Jackson Chapter 2. Homework #7: None. |
| Fri. Oct. 5, 2012 |
Lecture: Bessel Functions, use
LectureScribe
to read the following files: FirstTry.lec, SecondTry.lec, Page1.lec, Page2.lec, Page3.lec, Page4.lec, Page5.lec, Page6.lec, Page7.lec. Homework #7: Jackson 3.10. Hints |
| Mon. Oct. 8, 2012 |
Lecture: Discussion of Test #2. How to solve boundary value problems
involving cylinders. Homework #8: Jackson 3.12. |
| Wed. Oct. 10, 2012 |
Lecture: The Mean Value Theorem and the Method of Relaxation. Homework #8: Griffiths 3.1. |
| Fri. Oct. 12, 2012 |
Test #2b. Covers Jackson Chapter 2. Homework #8: None. |
| Mon. Oct. 15, 2012 |
Lecture: Multipole expansion and correspondence between Cartesian and
Spherical multipole tensors. Homework #9: Jackson 4.1. |
| Wed. Oct. 17, 2012 |
Lecture: Integral of the Electric field over a sphere: 1. Case of the external field of a dipole in the sphere. 2. Case of fields generated externally to the sphere. 3. The general case including charges in the sphere. Homework #9: Jackson 4.2. |
| Mon. Oct. 22, 2012 |
Lecture: Integral of electric field in a sphere (continued). Energy of
a charge distribution in an external electric field. Homework #10: Jackson 4.5. |
| Wed. Oct. 24, 2012 |
Lecture: Interaction energy of two dipoles. Introduction to
dielectrics. Polarization and displacement fields. Molecular
polarizability, susceptibility, permittivity and the dielectric
constant. The relation D = ε E. Modified Maxwell
equations. Boundary conditions for dielectrics. E, P,
and D in a permanently polarized dielectric and why the
relation D = ε E "fails" there. Homework #10: Jackson 4.7. Hints |
| Fri. Oct. 26, 2012 |
Lecture: Electric field strength in a dielectric. Electric field lines
at the boundary between two dielectrics. Boundary value problems
involving dielectrics. Homework #10: Jackson 4.10. |
| Mon. Oct. 29, 2012 |
Lecture: Fields in a dielectric sphere and cylinder immersed in an
initially uniform electric field. Molecular polarizability for polar
and non-polar molecules. Energy density for a field in a dielectric. Homework #11: Calculate the total energy inside a sphere of radius R containing a uniform electric field of strength E0. Repeat your calculation for the case when a small dielectric sphere of radius a (a ‹‹ R) is placed at the center. Which configuration has the lower total energy, and by how much? Hints |
| Wed. Oct. 31, 2012 |
Lecture: Introduction to Magnetostatics:
|
| Fri. Nov. 2, 2012 |
Lecture: General solution for A in terms of an integral over the
source J. Multipole expansion of A, and result for the dipole term. Homework #11: Jackson 5.8. |
| Mon. Nov. 5, 2012 |
Lecture: Magnetic dipole term for the vector potential due to a
current distribution. Magnetic field due to such a potential. Delta
function at the origin for a point magnetic dipole located at the
origin. Magnetic moments of charged elementary particles (a) in motion (b) due to
their spin. Homework #12: Jackson 5.7. |
| Wed. Nov. 7, 2012 |
Lecture: Magnetic and electric dipoles: potential and field due to
these, force on these when placed in a field, torque on these, induced
dipoles. Vector potential due to magnetized materials, bound currents,
the field H. Homework #12: Jackson 5.19. |
| Fri. Nov. 9, 2012 |
Lecture: Boundary conditions at the interface of two magnetic
materials. Discussion of types of Magnetic Materials. Homework #12: What is the equivalent of Snell's Law for magnetic field lines at the interface of two magnetic materials? |
| Mon. Nov. 12, 2012 |
Lecture: Magnetic field of a uniformly magnetized sphere inside and
outside the sphere solved using (a) the magnetic vector potential and
(b) the magnetic scalar potential. Homework #13: Jackson 5.22. |
| Wed. Nov. 14, 2012 |
Test #3. Covers Jackson Chapters 3, 4, and Chapter 5 up to and
including equation (5.55). Homework #13: None. |
| Fri. Nov. 16, 2012 |
Lecture: Faraday and his Law. Homework #13: Jackson 5.33. |
| Mon. Nov. 19, 2012 |
Lecture: The problem with Ampere's Law and Maxwell's fix for it. Wave
equations for potentials. Homework #14 [Due on Monday, 11/26]: Jackson 5.26. |
| Mon. Nov. 26, 2012 |
Lecture: Green Function for electrodynamics potentials in the Lorenz gauge. Homework #15 [Due on Monday, 12/3]: Griffiths 7.58. |
| Wed. Nov. 28, 2012 |
Lecture:
The retarded and advanced Green functions and solutions for
the potential using the retarded Green function. Homework #15 [Due on Monday, 12/3]: None. |
| Fri. Nov. 30, 2012 |
Lecture:
Solutions for the electrodynamics potentials in the case of
moving sources. Homework #15 [Due on Monday, 12/3]: Griffiths 10.9. |
| Mon. Dec. 3, 2012 |
Lecture: The electrodynamics potentials for a charge in motion
(Lienard-Wiechert potentials). The particular case of a charge in
uniform motion. The electromagnetic fields for time-dependent sources. Homework #16 [Due on Friday, 12/7]: Griffiths 10.13. |
| Wed. Dec. 5, 2012 |
Lecture: The life of Oliver Heaviside. The Poynting vector and its
divergence. Poynting vector in the context of an electromagnetic
wave. The Maxwell Stress Tensor: its definition and tensor
properties. The electromagnetic force per unit volume. Homework #16 [Due on Friday, 12/7]: Jackson 6.4. |
| Fri. Dec. 7, 2012 |
Lecture: More on the Maxwell Stress Tensor. Course review and discussion for Final Exam. Homework: None. |
| Tue. Dec. 11, 2012 9:00 AM - 11:30 AM | FINAL EXAM: Covers ALL material! |
,
K da and J dV. Why we must be careful to place the vector
sign on K (as opposed to da) and with the apellations "areal" and "volume" for the
current densities K and J, respectively.