Lecture Notes from PHYS606 - Electrodynamics, as taught by Dr. Thomas Antonsen in the Spring, 2016 semester. Lecture 1 (01/28/16): Introduction & Fundamentals - Electrostatics - Coulomb's Law - Gauss' Law - Re-expressing Coulomb's Law Lecture 2 (02/02/16): Topics in Electrostatics Guest Lecturer: Dr. Phillip Sprangle - Charge Distribution & Field Contributions - Forces on Conductors: Electrostatic Pressure - Coulomb's Law, Laplace's Equation, and Poisson's Equation - Green's Theorem - Boundary Conditions on Poisson's Equation - Uniqueness of Solutions to Poisson's Equation - Green's Function - Electrostatic Potential Enegry - Capacitors Lecture 3 (02/04/16): Approaches to Solving Electrostatics - Boundary Conditions - Forces on Conductors - Reciprocity of Green's Functions G(x,x') - Variational Approaches Lecture 4 (02/09/16): Method of Images - General Method of Images - Method of Images for Point Charges - Solutions Using Superposition - Method of Images for Line Charges - Non-Convergant Systems Lecture 5 (02/11/16): Solutions to Fields & Enhancements - Non-Convergant Systems - Field Enhancements - Solving Line Charges - Solutions in Grooves or at Blade Points - Spherical Harmonics Lecture 6 (02/16/16): Spherical Electrostatics - Spherical Harmonics - The Rodriguez Equation - Bounded Spaces - Laplace's Equation in Spherical Coordinates - Conducting Sphere - Point Charge Above a Cone Lecture 7 (02/18/16): Multipoles & Dielectrics Guest Lecturer: Dr. Marc Swisdak - Multipoles & Multipole Moments - Dipole Field - Potential Energy of a Multipole Expansion - Dielectrics - Displacement - Boundary Conditions Lecture 8 (02/23/16): Ponderable Materials & Dielectrics - Basics of Ponderable Materials - Macroscopic Treatment of Dipoles - Electric Polarization & Displacement - Linear Material Approximation - Dielectric Sphere in an Applied Field - Permanently Polarized Sphere - Polarization Density & Resonance - Clausius-Mosotti Lecture 9 (02/25/16): Polarization & Conductivity - Simple Model of Polarizability - Kramers-Kronig Relation: frequency dependence - Cauchy's Theorem - Energy Stored in Media (lossless dielectric) - Foster's Theorem - Oscillating Fields - Electrical Conductivity - Current & Conductors - Conservation of Charge Lecture 10 (03/01/16): Properties of Conductivity - Ohm's Law - Drude Model of Conductivity - Boundary Conditions - Resistance of a Conductor - Current Flow Past a Void - Child-Langmuir Law -----------------END OF MIDTERM I MATERIAL------------------------- - Introduction to Magnetostatics Lecture 11 (03/03/16): Magnetostatics - Basics of Magnetostatics - Vector Potential - Ampere's Law - Coulomb Gauge - Biot-Savart Law - Fields due to Localized Current Distributions Lecture 12 (03/08/16): Applications of Magnetostatics - Fields from Localized Current Distributions - Force Due to Current Through a Loop - Magnetic Moment Propagation - Force & Torque on Dipoles in an External Field - Magnetic Moment & Angular Momentum - Magnetic Materials (Magnetization) - Boundary Conditions: Using Constituative Relations - Magnetostatics Problems Lecture 13 (03/10/16): Time-Variable Magnetics - ex. Permeable Sphere in a Constant Magnetic Field - ex. Uniformly Magnetized Sphere - Faraday's Law & Ampere's Law - Stationary Loops - Moving Loops - Induced Current - Self-Inductance - The Skin Effect (Skin Depth) Lecture 14 (03/22/16): Applications of Changing Magnetic Fields - The Skin Effect - Attenuation Rate - Magnetic Dynamo - Building a Kinematic Dynamo - Displacement Current - Scalar & Vector Potentials Lecture 15 (03/25/16): Retarded Potentials & Conservation - Retarded Potentials - The Gauge Condition - Green's Function for the 3D Wave Equation - ex. Oscillating Current Density - Conservation of Energy & Momentum - Poynting Flux - Mechanical Momentum & The Electromagnetic Stress Tensor Lecture 16 (03/29/16): Properties of Electromagnetic Waves Guest Lecturer: Dr. Edward Ott - Time Harmonic Fields - The Helmholtz Equation - Electromagnetic Plane Waves - Phase Velocity - Poynting Vector - Dispersive vs. Non-Dispersive Media - Group Velocity - Fourier Transforms Lecture 17 (03/31/16): Behavior of Electromagnetic Plane Waves - Plane Waves & The Dispersion Relation - Dispersion - Polarization - Dissipation - Pulse Propagation - Time & Phase Delay - Instantaneous Frequency Lecture 18 (04/05/16): Diffraction and the Parabolic Wave Equation - Jackson Problem 7.14(a) - Dispersion - Diffraction - Beam Spreading - ex. Rectangular Aperture - The Parabolic Wave Equation - Geometric Optics (Hamilton's Equations) Lecture 19 (04/07/16): Reflections & Interfaces - Geometric Optics (Evolution of Trajectory) - Index of Refraction - Reflections at Interfaces - Normal vs. Oblique Incidence - Transverse Electric (TE) & Transverse Magnetic (TM) Waves - Transmission Coefficient - Brewster's Angle & Critical Angle -----------------END OF MIDTERM II MATERIAL------------------------- - Guided Waves - Metallic Wave Guides Lecture 20 (04/12/16): Guided Waves - Field Decomposition - Modes: TE & TM (Metallic Waveguides) - ex. Transverse Magnetic Wave - ex. Rectangular Wave Guide - TEM Modes - Attenuation Lecture 21 (04/14/16): Attenuation in Waveguides - Attenuation due to Bulk Losses - Attenuation due to Wall Losses - The Waveguide Anthropic Principle & Poynting's Theorem - Characterizing Mode Dependence (Frequency Dependence) - Optical Guiding by Total Internal Reflection - ex. Slab of Dielectric Material (Even & Odd Modes) Lecture 22 (04/19/16): Radiation Guest Lecturer: Dr. Phillip Sprangle - Derivation of Radiation Expressions & Approximations - Radiation Intensity & Power - Electric and Magnetic Dipole Radiation - Center-Fed Linear Antenna - Antenna in the Dipole Limit - Radiation from Moving & Accelerating Charges - Larmor's Formula - Radiation from Multiple Charges - Thermal & Laser Radiation - Single Mode & Multimode Laser Sources Lecture 23 (04/26/16): Relativity: Motion & Fields Guest Lecturer: Dr. Adil Hassam - Covariance & Manifest Covariance - Galilean Transformations - Equivalence of Inertial Frames - Inspection of Maxwell's Equations - Lorentz Transformation & the Lorentz Factor - Modified Newton's Equations Lecture 24 (04/28/16): Four-Vectors - Review of Relativistic Motions & Fields - Lorentz Transformation in 4 Variables - Invariant Separation - Proper Time - Four-Vectors as Invariant Quantities - ex. The Gyrotron Lecture 25 (05/03/16): Relativistic Energy Conservation - Energy-Momentum 4-Vector - Conservation in an Elastic Collision - Conservation in the Center of Mass Frame - The Accelerator Problem/Threshold Calculation - Compton Scattering - Hamiltonian Formulation of Relativistic Motion - Hamiltonian as a Constant of Motion - ex. Charged Particle in a "Wiggler" Periodic Magnetic Field - Synchrotron Radiation Lecture 26 (05/05/16): Contravariant & Covariant Components - Continuing Hamiltonian Formulation of Relativistic Motion - Relativistic Action - Covariant & Contravariant Components - The Metric Tensor - Radiation from Steady Oscillating Currents - Transient Radiation from Accelerated Charges - Metallic Antenna - Antenna Gain - Reciprocity