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Matter & Interactions Vol II: Electric & Magnetic Interactions Ruth Chabay & Bruce Sherwood This project was supported in part by the National Science Foundation (Grants MDR-8953367, USE9156105, DUE-9954843, and DUE 9972420). Opinions expressed are those of the authors, and not necessarily those of the Foundation. Note This presentation is normally accompanied by oral clarifications. However, it may be useful as it stands to give an overview of the nature of Volume II of Matter & Interactions. Homework problems displayed in this presentation are copyright John Wiley & Sons. E&M What’s new for students? • Concept of electric and magnetic fields • More sophisticated model of matter Field • More abstract than force • Allows us to explain and predict phenomena which otherwise would be inaccessible Model of Matter • Previously: neutral masses (atoms) connected by springs (bonds) • Now: consider individual charged particles inside matter (electrons, nuclei) What’s not new? • Small number of powerful fundamental principles (unification) • Modeling complex physical systems (idealization, approximations) • Integrated activities (desktop experiments, computer labs) Traditional sequence: three unrelated topics 1. Charge, force, field, flux, Gauss’s law (2 weeks!) 2. Current, potential, circuits 3. Magnetic field, magnetic force, magnetic induction Deficiencies of traditional sequence • Three unrelated topics - no unification • Many new abstract concepts introduced too fast, with insufficient practice • Magnetic field introduced late in semester, after many other new concepts At end of semester, students still confused about the difference between charge and field. EMI sequence • Field: – Introduced early, used continually – Backbone of story line, always salient • Matter: – Fields affect matter – Composed of charged particles – Mobile charges are important Solidify field concept • • • • • • Introduced on first day Central concept throughout course B introduced very early Retardation Patterns of field in space important Reference frames - relation of E & B Unification • DC, RC circuits analyzed in terms of charge, field and energy (potential) • Fundamental principles same as in mechanics Energy principle: ΔVroundtrip 0 Stationary charges Sequence of chapters • Electric field • Matter and electric fields • Electric field of distributed charges • Electric potential • Magnetic field • A microscopic view of electric circuits • Capacitors, resistors, & batteries • Magnetic force • Gauss, Ampere • Faraday’s law • Electromagnetic radiation • Waves and particles • (Semiconductor devices) Not all patterns of field are possible Energy Conservation No curly E • (stationary point charges) dV 0 Relate observed patterns of field to source charge (Gauss, Ampere) No divergent B dB curly E dt dE curly B dt (Faraday) (Ampere-Maxwell) Cognitive Issues • Primacy: E & B introduced early – Learn concept well - continued practice – Learn relationship of E & B through tasks involving both • Recency: Just-in-time flux – Gauss’s law only after much practice with q & E – Gauss’s law just before Faraday’s law Gauss’s Law (a pedagogical case study) • Parsimonious – very few steps in reasoning required • Elegant – symmetry instead of algebra • Abstract and powerful • Relativistically correct Gauss’s Law in Introductory E&M First or second week of E&M in the traditional introductory course. Used to derive: • E of a uniform spherical shell, plate, rod • No excess charge in interior of a conductor • E = 0 inside hole in a conductor Students are rarely able to understand or apply Gauss’s Law. Why? What knowledge is necessary to understand Gauss’s Law? • Calculus • Physics • Symmetry / geometry Calculus Students have not yet studied vector calculus E 0 Calculus Students have not yet studied surface integrals qinside E nˆdA 0 Students have not yet encountered vectors inside integrals Calculus Mathematically formal, unfamiliar, and intimidating Physics Gauss’s law relates patterns of electric field in 3D space to spatial distributions of source charges Physics Electric Field: • New concept • Abstract, still unfamiliar • Students still vague on relation between charge and field Physics Electric field • Students have little or no experience with possible patterns of electric field • Have calculated E only at a single location • Students have no experience thinking in 3D Symmetry • Students have a lot of practice in algebra (To them, this is physics reasoning) • Students have never before encountered a symmetry argument! Although symmetry arguments are powerful, they are not obvious or intuitive without explicit instruction and practice • Students have no experience thinking in 3D Maximizing the chances of learning • Introduce Gauss’s Law later, after students have more experience with electric field • Give students more experience with patterns of electric field in space • Use 2D and 3D visualization tools • Introduce relationships qualitatively • Connect qualitative, visual representations to math Gauss’s Law in Matter & Interactions Field as primary concept throughout semester Work with field and patterns of field for 15 weeks Delay Gauss’s Law until week 9 Who benefits from early introduction of Gauss’s Law? Introduce qualitatively, visually See instructor programs at M&I web site Limited goals Visualization of Flux Confusion: Gauss’s Law and Superposition Principle (appears that E on surface is due only to q inside) 5-10 minute lecture-demonstration (EMField) Students spontaneously draw diagrams like those in EMField Final exam problem at CMU Electron current i enters steady state circuit u1 > u2 and n1 > n2 Dashed line: Gaussian surface with circular cross section and radius < r Determine amount and sign of charge on the interface between the Cu and NiCr wires. Final exam problem: Gauss’s Law mean = 19 / 25 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 Electromagnetic Radiation • Central to course (this is the punch line) • Radiative fields affect matter in the usual way • Produced by accelerated charges • Microscopic mechanism for physical optics (re-radiation) Modeling in EMI • • • • • • • • Amount of charge on a tape Sparks in air (initial model fails) Pick up Al foil Polarizability of C Magnetic moment of bar magnet Cyclotron Semiconductor devices … Computer programs written by students, using VPython Field of a dipole Motion of proton in a dipole field Field of a charged rod Field inside & outside a solenoid Cyclotron Positron in a plane wave Matter & Interactions I: Modern Mechanics modern mechanics; integrated thermal physics Matter & Interactions II: Electric & Magnetic Interactions modern E&M; physical optics Ruth Chabay & Bruce Sherwood John Wiley & Sons, 2002 http://www4.ncsu.edu/~rwchabay/mi