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SPRING 2015 Department of Physics & Astronomy, UGA PHYS 4202/6202 Electricity and Magnetism II (as of Jan. 03/2015) The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary. Course Description: Oasis Title: Prerequisite: Grading System: Instructor: Office: Email: Sections: Office hours: Main text: Useful text: Academic Honesty: Attendance: Homework: Midterm exams: Final exam: Grading policy: Cut-offs: How to do well in this class: Topics include Maxwell's equations, electromagnetic radiation, the theory of electromagnetic fields in matter, and Einstein's special theory of relativity. ELEC & MAGNET II PHYS 4201/6201 A-F (Traditional) Dr. Andrei Galiautdinov 220 [email protected] 27333/27337 09:05a - 09:55a MWF 09:55a - 10:55a MW Your lecture notes D.J. Griffiths, Introduction to Electrodynamics, 4th Edition (Pearson, 2013) As a University of Georgia student, you have agreed to abide by the University’s academic honesty policy, “A Culture of Honesty,” and the Student Honor Code. All academic work must meet the standards described in “A Culture of Honesty” found at: www.uga.edu/honesty. Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor. Absolutely mandatory - No make-ups; collaboration while solving OK; submission & discussion individual - PHYS4202 students submit on paper before deadline - PHYS6202 students submit on paper before deadline, then make an appointment to discuss with instructor None - Mandatory - Closed notes, closed book - A simple (non-graphing, non-symbolic, non-programmable) scientific calculator - No other electronic device(s) permitted - Must work individually 10% ATTENDANCE & PARTICIPATION 60% HMWK (must be submitted before deadline, no make-ups; graduate students must discuss their graded HMWK solutions with instructor before the assigned grade goes into effect) 30% FINAL EXAM (mandatory, cumulative, no make-ups) F: [0, 60) D: [60, 68) C-: [68, 70) C: [70, 75) C+: [75, 78 ) B-: [78, 80) B: [80, 85) B+: [85, 88) A-: [88, 90) A: [90, 100] NOTE: No rounding; 89.99 = A-, etc. 1. Read about the material to be covered in class before coming to lecture. 2. Attend every lecture. 3. Ask questions. 4. Participate actively in discussions. 5. Re-read (or better re-work) your notes after class. 6. 7. 8. 9. 10. 11. Do assigned homework. Use a buddy system: find a friend with whom to discuss physics. Think about physics on a regular basis. Think about physics as much as possible. Think about physics at all times. If you decide to stay in academia, you will be competing against fanatics; so prepare early. 12. If everything fails, consider dropping the class before the deadline and retaking it at a later time. NOTE: In physics, learning can be frustrating and nonlinear. Often you have to work for a long time (many days and even weeks) without feeling that you are making much progress. Then, suddenly, everything falls into place and it all makes sense. But until the “click,” you can’t be sure how much time you need to “get it” and it’s difficult to plan… As you solve a physics problem, stop and ask yourself: What (exactly) are you doing? Why are you doing it? How does it help you? Spring 2015 Schedule Week 1 Day M Date Jan. 05 Reading Topic PART 1: MAGNETOSTATICS IN THE PRESENCE OF MATTER 2 T W Jan. 06 Jan. 07 R F Jan. 08 Jan. 09 M Jan. 12 T W Jan. 13 Jan. 14 p. 220 8.1.1 5.2.1 5.4.1,3 Demos (cont.) Graphical and calculational examples (cont.) Coordinate independent definitions of divergence and rotor ED: The meaning of current density j ED: (Local) charge conservation & continuity equation MS: Steady currents confined to finite volume MS: Magnetic vector potential A VC: The meaning of the Laplacian MS: Formula for magnetic vector potential A MS: Restriction on j MS: Magnetic dipole moment (preliminary discussion) MS: Magnetic dipole moment of a planar loop with current (preliminary discussion) MS: Multipole expansion of the vector potential (up do dipole - intro) R F Jan. 15 Jan. 16 ED: Classical electrodynamics overview ED: Operational definition of electric & magnetic fields ED: Maxwell’s equations in local & integral form (and brief discussion of where they come from) Lorentz-Heaviside force law Demos Graphical and calculational examples (cont.) 3 M T W Jan. 19 Jan. 20 Jan. 21 R F Jan. 22 Jan. 23 F Jan. 26 MLK Day 4 6.1.1-4 6.2.1-3 6.3.1-3 6.4.1-2 T W Jan. 27 Jan. 28 R F Jan. 29 Jan. 30 M Feb. 02 5 T W R F M 6 Feb. 03 Feb. 04 Feb. 05 Feb. 06 Feb. 09 VC: “Rotor of a vector product” formula MS: Magnetic field of a magnetic dipole MS: Magnetic field of a straight current (quick derivation from Maxwell’s 4th equation) MM: Ampere’s hypothesis MS: Magnetic dipole moment of a plain loop with current MS: Magnetic dipole moment of an orbiting electron in the H-atom MS: Some simple estimates MECH: Review of work, energy, Work-kinetic-Energy Theorem (WkET), the Law of Conservation of mechanical Energy (LCE) MS: Behavior of a magnetic dipole in the magnetic field: torque, energy, force MS: Conceptual introduction to magnetism in matter MS: Demo: Diamagnetic response MS: Magnetization, M(r) MS: The starting formula for calculation of magnetic vector potential A(r) of a magnetized object MS: Magnetic field of an infinitely long solenoid with current. MS: Magnetic vector potential A(r) of a magnetized object MS: Magnetic vector potential A(r) of a magnetized object (cont.) VC: Divergence Theorem; Modified Divergence Theorem VC: Cylindrical coordinate system MS: Prob. 6.7. Infinitely long uniformly magnetized cylinder MS: Prob. 6.8. Infinitely long non-uniformly circularly magnetized cylinder (intro) MS: A remark on old-fashioned magnetic core memory MS: Prob. 6.8. Infinitely long non-uniformly circularly magnetized cylinder (cont.) MS: Maxwell’s equations in the presence of magnetics MS: Paramagnetics, diamagnetics, magnetic susceptibility MS: Maxwell’s equations in the presence of magnetics (cont.) MS: Paramagnetics, diamagnetics, magnetic susceptibility Example 1: Long solenoid filled with a magnetic Example 2: Long straight current immersed in a magnetic (cont.) PART 2: ELECTRODYNAMICS 7.1-3 8.*** Review of Maxwell’s Equations in a vacuum Faraday’s Law of Induction as a first step towards electrodynamics Lenz Rule Demos T W Feb. 10 Feb. 11 R F Feb. 12 Feb. 13 M Feb. 16 7 T W R F 8 Feb. 17 Feb. 18 Feb. 19 Feb. 20 Faraday’s Law of Induction (cont.) Units of various physical quantities Demo: Eddy currents; a falling magnet Some formal math stuff Example: Induced electric field inside of a solenoid with changing current (uniform time-dependent B-field) Examples: Conceptual stuff related to Lentz Rule Review of Maxwell’s Equations in a vacuum Existence of processes in which charge accumulation is possible Demo 1: Camera flash based on a capacitor Demo 2: Alternating current flows through the capacitor Maxwell’s correction (1864): Displacement current Complete system of Maxwell’s Equations (in a vacuum) Complete system of Maxwell’s Equations (in a vacuum) Local charge conservation as a consequence of ME Consistency of Maxwell’s equations; differential consequences* Law of Conservation of Energy in the presence of the electromagnetic field Poynting’s Vector Examples: Electromagnetic energy flow in various situations (cont.) PART 3: ELECTROMAGNETIC RADIATION (from slowly moving sources) M Feb. 23 T W Feb. 24 Feb. 25 EMF of a uniformly moving charge – Directly from the wave equation (cont.) R F Feb. 26 Feb. 27 M Mar. 02 EMF of a uniformly moving charge – Directly from the wave equation (cont.) Retarded potentials A note on the use of advanced potentials when boundary conditions at a finite distance from source have to be maintained. Plane EM waves generated by a uniform time-dependent planar current 9 T W Mar. 03 Mar. 04 Electromagnetic potentials Gauge invariance Differential equations for electromagnetic potentials The Lorenz gauge EMF of a uniformly moving charge – Directly from the wave equation Plane EM waves generated by a uniform time-dependent planar current (cont.) Intuitive understanding of radiation by an accelerated charge EMF of a linearly accelerated charge (graphical derivation in the non-relativistic limit in the radiation zone) 10 11 12 R F M T W R F M T W R F M T W Mar. 05 Mar. 06 Mar. 09 Mar. 10 Mar. 11 Mar. 12 Mar. 13 Mar. 16 Mar. 17 Mar. 18 Mar. 19 Mar. 20 Mar. 23 Mar. 24 Mar. 25 R F Mar. 26 Mar. 27 M Mar. 30 13 Spring Break EMF of a time-dependent point dipole (Model) EMF of a time-dependent point dipole (Potentials) Withdrawal deadline EMF of a time-dependent point dipole (E - field) EMF of a time-dependent point dipole (B - field) EMF of a time-dependent point dipole (Poynting’s vector) The blueness of the sky Jefimenko equations; alternative derivation of the dipole radiation formulae (if time permits) Special Relativity as a Theory of Space and Time Inertial reference frames, properties of space & time, relativity principle Derivation of Lorentz transformations (without Einstein’s 2nd Postulate) PART 4: RELATIVITY T W Mar. 31 Apr. 01 R F Apr. 02 Apr. 03 M Apr. 06 T W R F Apr. 07 Apr. 08 Apr. 09 Apr. 10 M Apr. 13 T W Apr. 14 Apr. 15 R F M T W R F Apr. 16 Apr. 17 Apr. 20 Apr. 21 Apr. 22 Apr. 23 Apr. 24 14 15 16 (cont.) Derivation of Lorentz transformations (without Einstein’s 2nd Postulate – cont.) Limiting speed Velocity addition formula Invariance of the limiting speed Speed of light Relativity of simultaneity Relativistic time dilation Length contraction Invariant interval Minkowski space-time 4-dimensional pseudo-Euclidean geometry 4-vectors, 4-tensors Relativistic dynamics 4-momentum, 4-force Relative velocity Applications to linear collisions Doppler’s effect Relativistic electrodynamics TBA TBA 17 18 19 M T W R F M T W R F M T Apr. 27 Apr. 28 Apr. 29 Apr. 30 May 01 May 04 May 05 May 06 May 07 May 08 May 11 May 12 TBA FINAL EXAM (8:00a-11:00a) Grades due (5 PM)