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The MIT TEAL Simulations and Visualizations in Electromagnetism

The MIT TEAL Simulations and Visualizations in Electromagnetism. John W. Belcher Kavli Center for Astrophysics and Space Research Department of Physics. Funding Sources NSF DUE-0618558 Davis Educational Foundation d’Arbeloff Fund iCampus Helena Foundation MIT Classes of 51, 55, 60.

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The MIT TEAL Simulations and Visualizations in Electromagnetism

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  1. The MIT TEAL Simulations and Visualizations in Electromagnetism John W. Belcher Kavli Center for Astrophysics and Space Research Department of Physics

  2. Funding Sources • NSF DUE-0618558 Davis Educational Foundation d’Arbeloff Fund iCampus Helena Foundation MIT Classes of 51, 55, 60

  3. Who Am I? PI on the Voyager Plasma Science Instrument on the Voyager Spacecraft I have spent a lot of time trying to explain the unseen to reporters at Voyager press conferences since 1979 I have taught E&M at all levels at MIT for 30 years I have helped reform freshman level E&M for the last six years Neptune’s Magnetosphere 1989

  4. A Brief Explanation of TEAL • How do visualizations fit into TEAL? • How do we represent fields: • Vector Field Grid • Field Lines (“Eppur Si Mouve”) • Line Integral Convolution (LIC)—the best thing since sliced bread • Moving Field Lines • When does this make sense? (E, B perpendicular) • What does it represent? (test particle motion) • Why it gives access to high level concepts, e.g. Maxwell stresses • Dynamic Line Integral Convolution and examples • How Does This Contribute to E&M Understanding? Outline of Talk

  5. TEAL: Technology Enabled Active Learning • Large freshman physics courses have inherent problems • Lecture/recitations are passive • No labs (at MIT) leads to lack of physical intuition • Math is abstract, hard to visualize (esp. E&M) • TEAL/Studio addresses these by • Replacing large lectures with interactive, collaborative pedagogy • Incorporating desk top experiments • Incorporating visualization/simulations

  6. One of the two MIT TEAL Classrooms Modeled after NCSU’s SCALE-UP Classroom

  7. Ideal TEAL Sequence • (instructor’s fantasy) • Lecture • Pre-Experiment Predictions • Experiment • Visualization of Experiment I will illustrate this sequence for Faraday’s Law

  8. 1. Lecture: Faraday’s Law Magnetic Flux Move down

  9. 2. Pre-Experiment Predictions Move down Magnetic Flux Personal Response System used for pre-experiment questions and responses

  10. 3. Experiment Experiment includes sliding an aluminum sleeve over the magnet and feeling the slowdown due to eddy currents

  11. 4.Visualization of Experiment • Show a virtual model of the real experiment • Add field representation • Show the field three ways: • Vector Field Grid • Field Lines • Line Integral Convolution

  12. Loop of wire has inductance L and resistance R and a decay time of L/R

  13. Line Integral Convolution (LIC) • Introduced by Cabral and Leedom (computer scientists) in 1993 • Uses a texture pattern where the streaks in the texture are parallel to the local field direction • Shows the structure of the field close to the resolution of the display! • Vastly superior to either vector field or field lines in showing structure of 2D fields

  14. Line Integral Convolution: How? • Take array of NxN pixels of random brightness • At any point, average the random pattern along a line in the direction of the local field for n pixels, n << N • Move to an adjacent new point and do this again • If you move parallel to the field to get to the new point, the resulting average is almost the same as for the old point, e.g. highly correlated • If you move perpendicular to the field to get to the new point, the resulting average is not correlated at all with the average at the previous point • This produces correlations along the field direction

  15. B average n pixels in direction of B B

  16. B B

  17. What does a LIC of this function look like? This function has zero divergence and non-zero curl, so you expect no sources and lots of circulation

  18. We had a full page of Wired Magazine devoted to one of these in Sept 2004

  19. Mapping Fields Applet (http://web.mit.edu/viz/soft/

  20. Moving Field Lines (nothing to do with plasma physics) Will the proton gyrating about the B field move with the solenoid if you slowly start pushing the cart? Why or why not? B

  21. Moving Field Lines (nothing to do with plasma physics) Yes the gyrating proton will move with the cart because of the ExB drift B V - - - - + + + + E space contraction!

  22. Moving Field Lines (nothing to do with plasma physics) Valid in situations where E and B are everywhere perpendicular In magneto-statics, field motion defined to be motion of test electric monopoles In electrostatics, field motion defined be motion of test magnetic monopoles Useful even in e.g. radiation because the motion is in the direction of the Poynting flux vector

  23. Moving Field Lines (nothing to do with plasma physics) In both the electrostatic and magneto-static case, for symmetric cases you can relatively easily get the motion of field lines simply by conserving flux in source free regions

  24. Moving Field Lines • Helps with higher order concepts, most obviously the flow of electromagnetic energy, but also the flow of electromagnetic momentum and the stresses transmitted by fields, that is, the Maxwell Stress Tensor • Fields transmit a pressure perpendicular to themselves and a tension parallel to themselves—that is you, can intuit their dynamical effects by looking at their shape!

  25. Moving Field Lines • Helps with higher order concepts, most obviously the flow of electromagnetic energy, but also the flow of electromagnetic momentum and the stresses transmitted by fields, that is, the Maxwell Stress Tensor • Fields transmit a pressure perpendicular to themselves and a tension parallel to themselves—that is you can intuit their dynamical effects by looking at their shape!

  26. Dynamic Line Integral Convolution • Can also impose the same field line motion defined above on the line integral convolution method by having the underlying random pattern move with the test particle drift velocity • This is called Dynamic Line Integral Convolution (DLIC), and was originated by Andreas Sundquist • Examples: • Falling Magnet • Oscillating Electric Dipole • Electric Dipole turning on • Light charges around heavy charge

  27. DLIC: Falling Magnet

  28. DLIC: Oscillating Electric Dipole

  29. DLIC: Turning On An Electric Dipole

  30. DLIC: Light charges around heavy charge Link to 1 Meg Avi Link to 10 Meg Avi The Seen Versus The Unseen

  31. Two Other Visualizations Electrostatic Video Game Interactive

  32. Two Other Visualizations Generating Plane Waves Interactive

  33. How Much Does This Contribute to E&M Understanding? • No clear evidence they are useful in the way we have been using them in TEAL • Need “Guided Inquiry” with these animations and visualizations, not just accessibility and exploration • Build the guided inquiry into e.g. Mastering Physics? • Carolann Koleci and I have been doing just that in a junior/senior Griffiths based course at WPI and plan to do a similar study in the corresponding course at MIT • Students have to use the visualizations to answer the Mastering Physics questions • We are just beginning to explore how to do this effectively and how to evaluate it

  34. Applications and software are open source http://web.mit.edu/viz/soft/

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