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SES # |
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TOPICS |
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READINGS |
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HOMEWORK |
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Lecture 1 |
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Introduction. Vectors, Index Notation for Scalar and Cross Products. The Symbols δij and εijk. Differential Vector Calculus. Gradient. |
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Griffiths: Chapter 1 – skip section 1.1.5 |
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Homework 1 is handed out |
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Lecture 2 |
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Divergence and Curl. Divergence of Curl, and Curl of Gradient. Gauss and Stokes Theorem. From E→ to Φ. Delta Functions as Singular Distributions of Charge. |
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Griffiths: Finish reading Chapter 1 |
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Recitation 1 |
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Questions on Homework #1. |
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Lecture 3 |
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Properties of Delta Functions. Delta Function in Spherical Coordinates. The Laplacian of 1/r. Coulomb’s Law and Calculation of the Electric Field. |
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Homework 2 is available |
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Lecture 4 |
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Deriving the Electrostatic Equations from Coulomb's Law. Scalar Potential, and E = -δV. Examples of use of Gauss's Law. Boundary Conditions for Electric Field. Conductors. |
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Griffiths: p. 58 -82 |
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Recitation 2 |
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Orthogonal Curvilinear Coordinates. Questions on Homework 2. |
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Lecture 5 |
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Electrostatic Energy for Discrete and Continuous Charge Distributions. Energy as ƒ|E|2. Comments on Self Energy. Force Computed by the Method of Virtual Displacement. Generalized Capacitance, Capacitors. |
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Griffiths: From p. 82 to end of Chapter 2 |
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Homework 2 due
Homework 3 is handed out |
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Lecture 6 |
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Uniqueness of Solutions. Green’s Theorem. Green’s Functions for the Dirichlet, Neumann and Mixed BV Problems. |
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Partial Material in Griffiths: p. 110-120 (you may consult Jackson sections 1.9 and 1.10, but it should not be really necessary) |
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Recitation 3 |
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Mean Value Theorem. Go over Homework 3. |
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Lecture 7 |
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Example of Dirichlet Green’s Function. Mean Value Theorem. Images and Conducting Spheres. Separation of Variables for Laplace’s Equation in Cartesian Coordinates. |
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Homework 3 due
Homework 4 is handed out |
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Lecture 8 |
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Griffiths: p. 121 -137 |
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Recitation 4 |
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Homework 4, Energy and Images. |
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Lecture 9 |
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The Case of Axial Symmetry, Finding the Basic Solutions rl Pl and r-(l+1)Pl . Generating Function for Legendre Polynomials. |
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Griffiths: p. 136 -145 |
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Homework 4, due
Homework 5 is handed out |
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Recitation 5 |
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Homework 5 Discussed. |
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Lecture 10 |
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Tensors Under Rotations. Multipole Expansion. |
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Griffiths: p. 146-155 |
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Homework 5 due
Hand out homework 6 |
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Lecture 11 |
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Dipoles, Quadrupoles. Azimuthal Symmetry. Magnetostatics, Charge Conservation and Magnetic Force. |
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Griffiths: p. 202-232 |
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Recitation 6 |
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Homework 6. |
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Lecture 12 |
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Biot-Savart Law. Magnetic Potential for Loops. Deriving the Basic Equations from the "Inverse Square Law". The Vector Potential A and the Coulomb Gauge ∇. Α = 0. |
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Homework 6 is due
Hand out Homework 7 |
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Lecture 13 |
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Ampere’s Law. Boundary Conditions for Magnetic Fields. Multipole Expansion of the Magnetic Field, Magnetic Dipoles. |
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Griffiths: p. 285-310 |
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Recitation 7 |
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Homework 7 Discussed. |
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Lecture 14 |
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Electromotive Force and Faraday’s Law. Inductance, Energy in Magnetic Fields, Maxwell Equations. |
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Griffiths: p. 310-328 |
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Homework 7 due |
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Test 1 |
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One hour and a half test on the material including up to Homework 7. |
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Lecture 15 |
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Energy in an External Electric Field. And Basics of Magnetostatics. |
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J: p. 142-143, and J: p. 168-177 |
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Homework 6 is handed out |
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Lecture 16 |
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Integral Forms for Magnetostatics. Magnetic Multipoles. Relation between Magnetic Moment and Angular Momentum. |
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J: p. 180-183 |
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Lecture 17 |
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Dielectrics. The Polarization Vector P and the Effective Charge Density and Surface Charge. The Modified Gauss’ Law in Terms of D and the Free Charge Density. Slits in Dielectrics. The Field of a Polarized Sphere. Clausius-Mossoti Equation. |
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J: p. 143-155 |
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Lecture 18 |
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Magnetic materials. Qualitative Discussion of Diamagnetism Paramagnetism and Ferro Magnetism. The Magnetization Vector Μ and its Effective Currents. The Magnetic Field Strength H. |
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Jackson: p. 187-191 |
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Homework 7 is handed out |
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Lecture 20 |
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Boundary Value Problems in Magnetostatics with and without Magnetic Materials. Magnetic Potential ΦM. A Uniformly Magnetized Sphere. And Faraday’s Law for Fixed Circuits. |
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Jackson: p. 191-197; p. 209-213 |
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Lecture 21 |
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Faraday’s Law for Moving Circuits. The Electromotive Force or emf. Maxwell’s Equations. Energy Conservation, Energy in the Electromagnetic Field and Energy Flow. Poynting’s Theorem and the Poynting Vector S. |
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Jackson: p. 217-219; p.236-237 |
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Lecture 22 |
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Momentum in the Electromagnetic Field. The Electromagnetic Stress Tensor Tij . Examples: Pressure, Force on a Conductor and Force on a Solenoid. Derivation of the Conservation Law. |
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Jackson: p. 238-239 |
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Homework 8 is handed out |
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Lecture 23 |
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Example: Spinning up a Charged Cylinder. Conservation of Angular Momentum and Flux of Angular Momentum. |
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Lecture 24 |
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Solutions of Maxwell Equations in Terms of Potentials. Gauge Transformations. The Lorentz Gauge and the Wave Equations for the Potentials. Green’s Functions for the Wave Equation. |
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Jackson: p. 219-226 |
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Homework 9 is handed out |
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Lecture 25 |
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Retarded Potentials. The Information Gathering Sphere. Plane Waves. Linear Polarization. Complex Vectors. |
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Jackson: p. 269-275 |
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Lecture 26 |
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Time Average of Bilinears. Energy Flow in Plane Waves. Circular and Elliptic Polarization. Phase and Group Velocities. Dispersion. |
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Jackson: p. 299-303. |
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Test 2 |
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Covers up to the Material in Homework 8. |
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Lecture 27 |
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Wave Propagation with Metallic Boundaries. Example: Modes in Rectangular Waveguides. TE Modes, cuto. Frequencies, the Dispersion Relation, Phase and Group Velocities. |
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Jackson: p. 339-346. Begin with Lienard-Wiechert Potentials |
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Lecture 28 |
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Derivation of the Lienard-Wiechert Potentials. The Fields of an Arbitrarily Moving Charge. The Fields of a Charge Moving with Constant Velocity. |
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Homework 10 is handed out |
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Lecture 29 |
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Fields of a Charge Moving with a Constant Velocity ν → c. The Radiation Term. Radiation from Oscillatory Charges. The Expansion of the Vector Potential . →A in Powers of d/λ. |
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Jackson: p. 391-394 |
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Lecture 30 |
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Electric Dipole Radiation. The Radiation Field, the Near Fields. Radiated Power. Example: Charge in Circular Motion. |
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Jackson: p. 394-401 |
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Lecture 31 |
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Finish Electric Dipole Radiation. Qualitative Aspects of Electric Quadrupole and Magnetic Dipole Radiation. |
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Lecture 32 |
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Special Relativity. Events, Intervals: Timelike and Spacelike. Proper Time. Lorentz Trans- formations. |
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Jackson: p. 506-521 or Landau and Lifshitz: p. 1-12 |
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Lecture 33 |
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Length Contraction Lorentz Tensors. The Invariant Tensors δνμ, εμνρσ and gμν. |
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Lecture 34 |
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The Four-Vectors Velocity, Acceleration, and Energy-Momentum. Particle Collissions. Relativistic Form of Electrodynamics. Particle Motion in Electromagnetic Fields. The F µν Tensor. |
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Jackson: p. 547-552 |
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Lecture 35 |
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Relativistic Form of Electrodynamics. The Four-Vector Potential and Maxwell Equations. The Stress Energy Tensor Tµν. Covariance. |
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Jackson: p. 604-606 |
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Final Exam |
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Closed Books and Closed Notes. Comprehensive, but with Emphasis in the Latter Part of the Course. |
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