PHY-6346 FALL SEMESTER Introduction and Survey The Inverse Square Law or the Mass of the Photon; Linear Superposition; Idealizations in Electromagnetism. Introduction to Electrostaties Coulomb's Law; Electric Field; Gauss's Law; Differential Form of Gauss's Law; Another Equation of Electrostatics and the Scalar Potential; Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential; Poisson and Laplace Equations; Green's Theorem; Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions; Formal Solution of Electrostatic Boundary-Value Problem with Green Function; Electrostatic Potential Energy and Energy Density; Capacitance. Boundary-Value Problems in Electrostatics : I Method of Images; Point Charge in the Presence of a Grounded Conducting Sphere; Point Charge in the Presence of a Charged; Insulated; Conducting Sphere; Point Charge Near a Conducting Sphere at Fixed Potential; Condgcting Sphere in a Uniform Electric Field by the Method of Images; Green Function for the Sphere; General Solution for the Potential; Conducting Sphere with Hemispheres at Different Potentials; Orthogonal Functions and Expansions. Separation of Variables, Laplace Equation in Rectangular Coordinates; a Two-dimensional Potential Problem, Summation of a Fourier Series; Fields and Charge Densities in Two-dimensional Corners and Along Edges. FIRST MIDTERM TEST Boundary-Value Problems in Electrostatics: II Laplace Equation in Spherical Coordinates; Legendre Equation and Legendre Polynomials; Boundary-Value Problems with Azimuthal Symmetry; Behavior of Fields in a Conical Hole or near a Sharp Point; Associated Legendre Functions and the Spherical Harmonics; Addition Theorem for Spherical Harmonics Laplace Equation in Cylindrical Coordinates, Bessel Functions; Boundary-Value Problems in Cylindrical Coordinates; Expansion of Green Functions in Spherical Coordinates; Solution of Potential Problems with Spherical Green Function Expansion; Expansion of Green Functions in Cylindrical Coordinates; Eigenfunction Expansions for Green Functions. Multipoles, Electrostatics of Macroscopic Media, Dielectrics Multipole Expansion; Multipole Expansion of the Energy of a Charge Distribution in an External Field; Elementary Treatment of Electrostatics with Ponderable Media; Boundary-Value Problems with Dielectrics; Molecular Polarizability and Electric Susceptibility; Models for the Molecular Polarizability; Electrostatic Energy in Dielectric Media. SECOND MIDTERM TEST Magnetostatics Biot and Savart Law; The Differential Equations of Magnetostatics and Amptre's Law; Vector Potential; Vector Potential and Magnetic Induction for a Circular Current Loop; Magnetic Fields of a Localized Current Distribution, Magnetic Moment; Force and Torque on and Energy of a Localized Current Distribution; Macroscopic Equations, Boundary Conditions on B and H; Methods of Solving Boundary-Value Problems in Magnetostatics; Uniformly Magnetized Sphere; Magnetized Sphere in an External Field, Permanent Magnets; Magnetic Shielding, Spherical Shell of Permeable Material in a Uniform; Field. Time-Varying Fields, Maxwell Equations, Conservation Laws Faraday's Law of Induction; Energy in the Magnetic Field; Maxwell's Displacement Current, Maxwell Equations; Vector and Scalar Potentials; Gauge Transformations, Lorentz Gauge, Coulomb Gauge; Green Functions for the Wave Equation; Macroscopic Electromagnetism; Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields; Conservation Laws for Macroscopic Media; Transformation Properties of Electromagnetic Fields and Sources under Rotations, Spatial Reflections, and Time Reversal; On the Question of Magnetic Monopoles; Dirac Quantization Condition. FINAL TEST ============================================================================== PHY-6347 SPRING SEMESTER Plane Electromagnetic Waves and Wave Propagation Plane Waves in a Nonconducting Medium; Linear and Circular Polarization, Stokes Parameters; Reflection and Refraction of Electromagnetic Waves at a Plane Interface between Dielectrics; Polarization by Reflection and Total Internal Reflection; Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas; Simplified Model of Propagation in the Ionosphere and Magnetosphere; Waves in a Conducting or Dissipative Medium; Superposition of Waves in One Dimension, Group Velocity; Illustration of the Spreading of a Pulse as It Propagates in a Dispersive; Medium; Causality in the Connection between D and E, Kramers-Kronig Relations; Arrival of a Signal After Propagation Through a Dispersive Medium. Wave Guides and Resonant Cavities Fields at the Surface of and within a Conductor; Cylindrical Cavities and Wave Guides; Modes in a Rectangular Wave Guide; Energy Flow and Attenuation in Wave Guides; Perturbation of Boundary Conditions; Resonant Cavities; Power Losses in a Cavity. Q of a Cavity; Earth and Ionosphere as a Resonant Cavity, Schumann Resonances; Dielectric Wave Guides. FIRST MIDTERM TEST Simple Radiating Systems, Scattering, and Diffraction Fields and Radiation of a Localized Oscillating Source Electric Dipole Fields and Radiation; Magnetic Dipole and Electric Quadrupole Fields; Center-fed Linea r Antenna; Scattering at Long Wavelengths, Perturbation Theory of Scattering, Rayleigh's Explanation of the Blue Sky; Scattering by Gases and Liquids; Scalar Diffraction Theory; Vector Equivalents of Kirchhoff Integral; Babinet's Principle of Complementary Screens; Diffraction by a Circular Aperture, Remarks on Small Apertures; Scattering in the Short-Wavelength Limit; Optical Theorem. SECOND MIDTERM TEST Special Theory of Relativity The Situation before 1900, Einstein's Two Postulates; Some Recent Experiments; Lorentz Transformations and Basic Kinematic Results of Special Relativity; Addition of Velocities, Four-Velocity; Relativistic Momentum and Energy of a Particle; Mathematical Properties of the Space-Time of Special Relativity; Matrix Representation of Lorentz Transformations, Infinitesimal Generators Thomas Precession; Invariance of Electric Charge, Covariance of Electrodynamics Transformation of Electromagnetic Fields; Notation and Units in Relativistic Kinematics. Dynamics of Relativistic Particles and Electromagnetic Fields Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields; Motion in a Uniform, Static, Magnetic Field; Motion in Combined Uniform, Static, Electric and Magnetic Fields; Particle Drifts in Nonuniform, Static Magnetic Fields; Adiabatic Invariance of Flux through Orbit of Particle. Collisions between Charged Particles, Radiation by Moving Charges Energy Transfer in a Coulomb Collision; Cherenkov Radiation; Litnard-Wiechert Potentials and Fields for a Point Charge; Total Power Radiated by an Accelerated Charge: Larmor's Formula and its Relativistic Generalization. FINAL TEST Units and Dimensions Units and Dimensions, Basic Units and Derived Units; Electromagnetic Units and Equations; Various Systems of Electromagnetic Units; Conversion of Equations and Amounts between Gaussian Units and MKSA Units.