All references to "Jackson" and "Griffiths" are to the third edition of the corresponding text.
| Day of week and Date | Lecture Content and Homework Assignment |
|---|---|
| Fri. Aug. 22, 2014 |
Lecture: Course outline, grading, other such matters (see course
website for details). Coulomb's Law. The Electric Field. Delta
Functions. Gauss's Law. Homework #1 (due Aug. 27, 2014): HW #1. |
| Mon. Aug. 25, 2014 |
Lecture: Gauss's Law. Coulomb's Law for the electric field utilized to
obtain an expression for the electric potential. Path independence of
the work done in moving a charge against an electric field. The
potential due to a surface dipole moment density. Homework #2 (due Sep. 3, 2014): HW problem. |
| Wed. Aug. 27, 2014 |
Lecture: The Poisson and Laplace equations. An integral form of the
Poisson equation, i.e., Jackson equation (1.36). Homework #2 (due Sep. 3, 2014): Jackson 1.5. |
| Fri. Aug. 29, 2014 |
Lecture: Uniqueness of solutions to the Poisson Equation. Solution via
the Green function method. Homework #2 (due Sep. 3, 2014): Jackson 1.12. |
| Tue. Sep. 2, 2014 |
Pre-poned Lecture (1 PM, Conference room): A discussion of methods and
problems in Griffiths Chapter 3. No homework. |
| Wed. Sep. 3, 2014 |
Lecture: Electrostatic energy in configurations of charges: both
discrete as well as continuous charge distributions. Energy density in
the electric field. Outward pressure on the surface of a conductor. Homework #3 (due Sep. 10, 2014): HW problem. |
| Fri. Sep. 5, 2014 |
Lecture: An equivalent integral formulation of the problem of finding
the electrostatic potential. Brief mention of the FEA method,
the relaxation method, and the trial function method to solve real
problems. Homework #3 (due Sep. 10, 2014): HW problem. |
| Mon. Sep. 8, 2014 |
Lecture: The method of images in the context of the integral
formulation of the electrostatics problem. Finding the potential for a point charge near a
grounded conducting plane and near a grounded conducting sphere. Using
the Green function to solve related problems. Homework #4 (due Sep. 17, 2014): Jackson 2.2. |
| Wed. Sep. 10, 2014 |
Lecture: Extending the Method of Images solution for a grounded
conducting sphere to the cases where the total charge on the sphere is
known or when the potential is known (and different from
zero). Beginning of the Green Function method (equation 1.42) solution of
the problem where the potential is specified on a grounded conducting
plane. Homework #4 (due Sep. 17, 2014): Jackson 2.4. |
| Fri. Sep. 12, 2014 |
Lecture: Green Function method (equation 1.42) solution of
the problem where the potential is specified on a grounded conducting
plane. Application to the specific case of finding the potential near
an infinite conducting plane for which a circular patch is held at a
fixed potential V0. Homework #4 (due Sep. 17, 2014): (a) Work out the Green Function method solution for the potential outside a conducting sphere on whose surface the potential is specified. This is section 2.6 of Jackson. Particular attention should be paid to arriving at equation (2.17) and the steps that follow to get to equation (2.18). (b) Consider a conducting sphere of radius R and centered on the origin with the potential Φ(x) = V0 cos(θ), where θ is the usual polar angle. Find the potential on the z-axis using the results of part (a). |
| Mon. Sep. 15, 2014 |
Lecture: Field near an uncharged conducting sphere immersed in a
uniform electric field. [Result up to two terms: constant field plus a
dipole field.] Homework #5 (due Sep. 24, 2014): Jackson 2.5. |
| Wed. Sep. 17, 2014 |
Lecture: Function spaces and basis functions. Solving the Laplace
equation by the method of separation
of variables. Application to a simple problem in Cartesian coordinates. Homework #5 (due Sep. 24, 2014): Jackson 2.23. |
| Fri. Sep. 19, 2014 |
Lecture: Solution to the Laplace Equation in Cylindrical Coordinates when there is
no z-dependence. The case of the potential near a sharp corner where
two conducting planes meet. Homework #5 (due Sep. 24, 2014): Jackson 2.13. |
| Mon. Sep. 22, 2014 |
Test #1: All material we covered up to and including on Mon., Sep. 15. No homework. |
| Wed. Sep. 24, 2014 |
Lecture: Solutions to the Laplace equation in spherical
coordinates. The general case and the case of azimuthal
symmetry. Using the latter solution to expand 1 / distance. Homework #6 (due Oct. 1, 2014): Jackson 3.1. |
| Fri. Sep. 26, 2014 |
Lecture: More on the Legendre Polynomials and the Spherical
Harmonics. Expansion of 1/distance, when the source is on the z-axis,
and also when it is not (using the Addition Theorem). Homework #6 (due Oct. 1, 2014): Jackson 3.4. |
| Mon. Sep. 29, 2014 |
Lecture: Solutions to the Laplace equation in cylindrical
coordinates. Bessel functions of first, second and third kind, and
Bessel functions with imaginary arguments (modified Bessel
functions). Homework #7 (due Oct. 8, 2014): Jackson 3.10. |
| Wed. Oct. 1, 2014 |
Lecture: Solutions to the Laplace equation in cylindrical coordinates
with various geometries and boundary conditions. Homework #7 (due Oct. 8, 2014): Jackson 3.12. |
| Fri. Oct. 3, 2014 |
Lecture: Definition of Cartesian and spherical multipole moments for a
localized charge distribution. Connection between the two types in the
=1 (dipole) case. The electric field of a dipole. Homework #7 (due Oct. 8, 2014): (a) Show that the lowest-order (in ) nonzero multipole moments are independent of the
choice of origin. (b) Connect the =2
spherical multipole moments with the quadrupole moments Qij
in Cartesian coordinates, i.e., derive equations (4.6) in Jackson.
|
| Mon. Oct. 6, 2014 |
Lecture: The integral of an electric field over the volume of a
sphere: (a) when there are no charges in the sphere and (b) when all
charges are in the sphere. Modification of the expression for the
electric field of a dipole: the δ-function term in the electric
field due to a "point" dipole and its meaning. Homework #8 (due Oct. 15, 2014): Jackson 4.7. |
| Wed. Oct. 8, 2014 |
Lecture: Energy of a charge distribution placed in an external
electric field. Polarization and dielectrics. Homework #8 (due Oct. 15, 2014): Jackson 4.5. |
| Fri. Oct. 10, 2014 |
Lecture: Energy of a dipole in an electric field, force on the dipole,
and torque on the dipole. Displacement field in dielectrics.
Permittivity, susceptibility, polarizability, dielectric constant.
Boundary conditions on D and E at an interface between two
dielectrics. Homework #8 (due Oct. 15, 2014): Griffiths 4.18, 4.19. |
| Mon. Oct. 13, 2014 |
Lecture: More on boundary conditions. Method of images for two
dielectric media with an infinite plane boundary. Homework #9 (due Oct. 22, 2014): (a) Justify the use of ε in place of ε0 for the potential due to a charge in an infinite linear dielectric medium. (b) Find equations for the field line curves in Fig. 4.5 (both halves) of Jackson, and also for the equipotential lines. |
| Wed. Oct. 15, 2014 |
Lecture: Fields in and near a dielectric sphere embedded in a uniform
electric field. Homework #9 (due Oct. 22, 2014): Obtain Jackson's equation 10.5. |
| Fri. Oct. 17, 2014 |
Lecture: Connection between the susceptibility and the molecular
polarizability for a solid. Introduction to magnetostatics. No homework. |
| Mon. Oct. 20, 2014 |
Lecture: Introduction to magnetostatics, continued: The Law of Biot
and Savart, and the Lorentz Force Law applied to currents. The
divergence of the magnetic field. The magnetic vector potential. Homework #10 (due Oct. 29, 2014): Griffiths 5.8. |
| Wed. Oct. 22, 2014 |
Test #2: All material we covered up to and including on Fri., Oct. 10. No homework. |
| Mon. Oct. 27, 2014 |
Lecture: Discussion of Test #2 results. Maxwell equations for the
magnetostatic magnetic field. Gauge freedom for the vector potential. Homework #11 (due Nov. 5, 2014): Derive (a) Jackson's equation (5.11) from (5.10) and (b) Ampere's Law, which he writes as equation (5.25), from his equation (5.22). |
| Wed. Oct. 29, 2014 |
Lecture: The magnetic field of a current loop using a magnetic scalar potential. Homework #11 (due Nov. 5, 2014): Jackson 5.4. |
| Fri. Oct. 31, 2014 |
Lecture: Multipole expansion of the vector potential in magnetostatics. Homework #11 (due Nov. 5, 2014): Jackson 5.7. |
| Mon. Nov. 3, 2014 |
Lecture: The integral of a magnetic field over a spherical volume for
(a) internal sources and (b) external sources. Modification of the
expression for the magnetic field of a dipole: the δ-function
term in the magnetic field due to a "point" dipole and its meaning.
The magnetic moment of charged particles, and the g-factor. Homework #12 (due Nov. 12, 2014): Complete all the steps in the derivation of Jackson's equation (5.69) from (5.66) and of Jackson's equation (5.71) from (5.70). |
| Wed. Nov. 5, 2014 |
Lecture: Bound volume and surface current densities in magnetized
materials. Comparison of expressions for electric and magnetic dipoles
(potentials, fields, energy, force on, torque on, polarization /
magnetization, Maxwell equations, bound volume and surface source
densities). A bit of history of electromagnetic fields. Homework #12 (due Nov. 12, 2014): Jackson 5.13. |
| Fri. Nov. 7, 2014 |
Lecture: Boundary conditions for magnetostatic fields. Implications
for the field direction immediately outside magnetized materials and for
the field direction immediately inside a magnetic material when the
field outside is determined, e.g., by a current. Hysterisis curve for
a ferromagnetic material, and large values of relative permeability
(100 to a million) for ferromagnetic materials. The magnetic
field for a magnetized ferromagnetic material using a scalar potential
and using a vector potential. Homework #12 (due Nov. 12, 2014): Jackson 5.14. |
| Mon. Nov. 10, 2014 |
Lecture: Magnetic fields inside and outside a uniformly magnetized
sphere: solution using scalar and vector magnetic
potentials. Hysterisis curves. Michael Faraday and his Law. Homework #13 (due Nov. 19, 2014): Jackson 5.15. |
| Wed. Nov. 12, 2014 |
Lecture: Faraday's Law in differential form, and the connection
between the curl of the electric field in the circuit and magnet
frames of reference. Mutual- and Self-Inductance. The energy in a loop
of current, and the energy density in a magnetic field. What's the
matter with Ampere's Law and Faraday's Law? The displacement current
solution to the missing term in Ampere's Law. Homework #13 (due Nov. 19, 2014): Jackson 5.22. |
| Fri. Nov. 14, 2014 |
Lecture: Adjusting the definition of the electric field to accomodate
time-dependent terms in the Maxwell equations. Exploiting gauge
invariance to cast the equations for the potentials in a streamlined
form, using the Lorentz-invariant Lorenz gauge. Homework #13 (due Nov. 19, 2014): No homework. |
| Mon. Nov. 17, 2014 |
Lecture: The 4-dimensional Green function for the electromagnetic wave equation. No homework. |
| Wed. Nov. 19, 2014 |
Test #3: All material we covered up to and including material in Chapter 5 of
Jackson. No homework. |
| Fri. Nov. 21, 2014 |
Lecture: The retarded Green function and retarded potentials for
stationary and moving sources. Homework #14 (due Monday Dec. 1, 2014): Griffiths 10.10, 10.14. |
| Mon. Nov. 24, 2014 |
Lecture: No lecture. Preponed to Tue. Sep. 2, 2014. No homework. |
| Mon. Dec. 1, 2014 |
Lecture: An introduction to electromagnetic waves. Homework #15 (due Friday Dec. 5, 2014): (a) Consider outgoing cylindrical and spherical waves. Provide expressions for their electromagnetic fields and compare these with corresponding expressions for plane waves. Show that at large distances from the source the cylindrical and spherical waves behave like plane waves. [Consider only the simplest expressions, no need to conisder multipoles in the source that lead to Hankel functions etc.] (b) Assuming the sun emits coherent waves at a fixed wavelength, say 589 nm, what is the energy density and Poynting vector for these waves at the sun's surface and at the earth's surface? What is the intensity? The electric and magnetic field strengths? [All answers should be specified in SI units, and the units should also be specified.] |
| Wed. Dec. 3, 2014 |
Lecture: Reflection and transmission of electromagnetic waves at a
boundary between two dielectric media. No homework. |
| Fri. Dec. 5, 2014 |
Lecture: The fraction of reflected and transmitted intensities (R and
T) for an electromagnetic wave incident on a boundary when the
polarization is (a) in the plane of incidence or (b) perpendicular to
the plane of incidence. No homework assigned, but it is suggested that you work out R and T for the two cases mentioned above and verify that their sum is unity. |
| Sat. Dec. 13, 2014 9:00 AM - 11:30 AM | FINAL EXAM: Covers ALL material! |