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Organizational issues,
general course description,
Maxwell's equations,
typical values of electric fields,
typical values of magnetic fields,
regime of applicability of classical E&M.
Charge quantization, Lorentz force,
Macroscopic media, Polarization, Magnetization,
relation between
D and
E,
relation between
B and
H,
Electric permittivity, Magnetic permeability,
Anisotropic media,
Boundary conditions at interfaces,
Tests of the inverse square law,
Cavendish's experiment,
Schumann resonances.
Laplace and Poisson equations,
Dirichlet and Neumann boundary conditions,
Green's theorem,
Electric dipole moments,
Discontinuity of
Φ across a layer
of dipoles.
Green functions
G(x,x')
for Poisson's equation with
Dirichlet or Neumann boundary conditions,
Example in one dimension.
Coefficients of potential,
Coefficients of induction,
Capacitances,
Electrostatic energy.
Point charge near an infinite conducting plane,
Point charge near a grounded conducting sphere,
Point charge near a charged conducting sphere,
Dirichlet problem for the space outside the sphere.
Method of Inversion,
Legendre Polynomials,
Legendre and Associated Legendre equations,
Spherical Harmonics,
Conducting sphere in a uniform electric field,
The WMAP Picture of the Cosmic Microwave Background.
Polar coordinates,
Behavior of electrostatic fields near corners and edges.
Legendre functions of the first kind,
Behavior of electrostatic fields near tips of cones.
Elliptical coordinates in 2D,
Oblate spherical coordinates in 3D,
Application to the problem of
a conducting plane with a circular hole.
Expansion of the potential in multipole coefficients.
Microscopic versus Macroscopic (mean) field,
Average electric field in a spherical region,
Clausius-Mossotti equation.
Vector potential,
Gauge invariance,
Coulomb gauge,
Bio-Savart law,
Force between current loops.
Magnetic dipole moment,
Field of a magnetic dipole,
Energy of a magnetic dipole in a magnetic field,
Force and torque on a magnetic dipole.
Energy density,
Poynting vector,
Energy conservation,
Electrostatic and Magnetostatic energy,
Self-Inductance,
Mutual-Inductance,
Ferromagnets,
Residual magnetic induction,
Coercive "force."
Electro-Magnetostatic Momentum density,
Momentum conservation,
Electro-Magnetostatic stress tensor,
A "gas" of photons,
The
Cosmic Microwave Background Radiation,
The 2006 Nobel Prize in Physics.
Expressions for
E and
B
in terms of the vector and scalar potentials
in the time-dependent case,
Gauge invariance in the time-dependent case,
The Lorenz gauge,
The Coulomb (transverse) gauge,
The inhomogeneous wave equation,
Helmholtz's equation,
Retarded and advanced potentials.
Helmholtz's equation,
Retarded and advanced potentials,
Green's function for the wave equation.
Electromagnetic field of a charged particle moving at constant velocity.
Cherenkov radiation,
Frank-Tamm formula for the radiated energy per unit distance along the path of the particle,
Ring Imaging Cherenkov (RICH) detectors,
The
Super-Kamiokande experiment,
(theoretical) proton decay.
(Midterm Survey), One-dimensional wave equation,
Plane waves, Linear and circular polarization, Phasors,
Averages of quadratic expressions.
Snell's law, Fresnel formulas, Total internal reflection,
Brewster angle, Goos-Haenchen effect.
Absorption coefficient,
Index of refraction and absorption coefficient of water,
Causality,
Kramers-Kronig relations.
Derivation of Kramers-Kronig relations,
Resonant absorption, Anomalous dispersion,
Plasma frequency, Plasma dispersion relation,
(Mass gap), Group velocity,
Propagation of plane waves through a dispersive medium,
Sommerfeld precursor.
...
...
...
Prof. Petr Hořava will talk about a particle in a magnetic field.
...
Prof. Raphael Bousso will talk about special relativity.
The antenna as a boundary value problem,
center-fed linear antenna,
radiated power, angular distribution.
skin depth,
duality relations for two electromagnetic systems with identical geometries,
the Gap Equation for a receiving antenna.
Lorentz transformations, proper Lorentz transformations, SO(3,1),
invariant interval, metric, 4-velocity, 4-acceleration,
momentarily comoving reference frame (MCRF).
Definition of tensors, transformation of tensors from one reference frame to another,
symmetric tensors, anti-symmetric tensors, field-strength tensor.
Field-strength tensor,
transformation of
E and
B,
4-current,
Maxwell's equations in tensor form,
4-potential, magnetization-polarization tensor,
Green's function for the wave equation
D(x,x').
Anomalous Zeeman effect,
spin-orbit interaction,
BMT equation,
measurement of the anomalous
gyromagnetic ratio
g
for the
electron,
Penning trap,
the 1989 Nobel prize in physics,
precession of the polarization,
measurement of the anomalous
gyromagnetic ratio
g
for the
muon
(the scientific paper is
arXiv:hep-th/0401008).