Field line motion in classical electromagnetism

American Journal of Physics

Volumn 71, Issue 3, 2003, Pages 220-228

  Belcher, John W ^a   Olbert, Stanislaw ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037342355     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1531577     Document Type: Article

References (32)

1. In one of his first papers on the subject, Maxwell remarked that "...In order therefore to appreciate the requirements of the science [of electromagnetism], the student must make himself familiar with a considerable body of most intricate mathematics, the mere retention of which in the memory materially interferes with further progress...," J. C. Maxwell, "On Faraday's lines of force," as quoted by T. K. Simpson, Maxwell on the Electromagnetic Field (Rutgers U.P., New Brunswick, NJ, 1997), p. 55.
2. E. F. Redish, "New models of physics instruction based on physics education research," invited talk presented at the 60th meeting of the Deutschen Physikalischen Gesellschaft, Jena, 14 March 1996, online at http://www.physics.umd.edu/perg/papers/redish/jena/jena.html
3. "...It appears therefore that the stress in the axis of a line of magnetic force is a tension, like that of a rope...," J. C. Maxwell, "On physical lines of force," as quoted by T. K. Simpson, Maxwell on the Electromagnetic Field (Rutgers U.P., New Brunswick, NJ, 1997), p. 146. Also "...The greatest magnetic tension produced by Joule by means of electromagnets was about 140 pounds weight on the square inch...," J. C. Maxwell, A Treatise on Electricity and Magnetism (Dover, New York, 1954), Vol. II, p. 283.
4. "...It appears therefore that the stress in the axis of a line of magnetic force is a tension, like that of a rope...," J. C. Maxwell, "On physical lines of force," as quoted by T. K. Simpson, Maxwell on the Electromagnetic Field (Rutgers U.P., New Brunswick, NJ, 1997), p. 146. Also "...The greatest magnetic tension produced by Joule by means of electromagnets was about 140 pounds weight on the square inch...," J. C. Maxwell, A Treatise on Electricity and Magnetism (Dover, New York, 1954), Vol. II, p. 283.
5. F. Hermann, "Energy density and stress: A new approach to teaching electromagnetism," Am. J. Phys. 57, 707-714 (1989).
6. R. C. Cross, "Magnetic lines of force and rubber bands," Am. J. Phys. 57, 722-725 (1989).
7. J. W. Belcher and R. M. Bessette, "Using 3D animation in teaching introductory electromagnetism," Comput. Graphics 35, 18-21 (2001).
8. See EPAPS Document No. E-AJPIAS-71-005302 for animations of the examples given in this paper. A direct link to this document may be found in the online article's HTML reference section. The document may also be reached via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps. See the EPAPS homepage for more information.
9. A description of the SCALE-UP program at North Carolina State University is available at 〈http://www.ncsu.edu/per/〉.
10. Y. J. Dori and J. W. Belcher, "Technology enabled active learning-Development and assessment," paper presented at the 2001 annual meeting of the National Association for Research in Science Teaching Conference, St. Louis, 25-28 March 2001.
11. "...Not only is it not possible to say whether the field lines move or do not move with charges-they may disappear completely in certain coordinate frames...," R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. II, pp. 1-9.
12. "...Also the idea of moving field lines is a priori suspect because the field should be regarded not as moving relative to the observer, but rather as changing in magnitude and direction at fixed points, as is proper...," R. H. Good, "Dipole radiation: A film," Am. J. Phys. 49, 185-187 (1981).
13. B. Rossi and S. Olbert, Introduction to the Physics of Space (McGraw-Hill, New York, 1970), p. 382.
14. V. M. Vasyliunas, "Non-uniqueness of magnetic field line motion," J. Geophys. Res. 77, 6271-6274 (1972).
15. J. W. Belcher, "The Jupiter-Io connection: An Alfven engine in space," Science 238, 170-176 (1987).
16. J. C. Hamilton and J. L. Schwartz, "Electric fields of moving charges: A series of four film loops," Am. J. Phys. 39, 1540-1542 (1971).
17. J. F. Hoburg, "Dynamic electric and magnetic field evolutions with computer graphics display," IEEE Trans. Educ. E-23, 16-22 (1980).
18. J. F. Hoburg, "Personal computer based educational tools for visualization of applied electroquasi-static and magnetoquasi-static phenomena," J. Electrost. 19, 165-179 (1987).
19. J. F. Hoburg, "Can computers really help students understand electromagnetics?" IEEE Trans. Educ. E-36, 119-122 (1993).
20. R. W. Chabay and B. A. Sherwood, "3-D visualization of fields," in The Changing Role of Physics Departments In Modern Universities, Proceedings of the International Conference on Undergraduate Physics Education, edited by E. F. Redish and J. S. Rigden, AIP Conf. Proc. 399, 763 1996.
21. S. C. Frautschi, R. P. Olenick, T. M. Apostol, and D. L. Goodstein, The Mechanical Universe (Cambridge U.P., Cambridge, 1986).
22. M. C. Salzman, M. C. Dede, and B. Loftin, "ScienceSpace: Virtual realities for learning complex and abstract scientific concepts," Proceedings of IEEE Virtual Reality Annual International Symposium (1996), pp. 246-253.
23. A. Wolf, S. J. Van Hook, and E. R. Weeks, "Electric field line diagrams don't work," Am. J. Phys. 64, 714-724 (1996).
24. This equation can be derived by considering the four dot product of the four momentum of the monopole with the dual field-strength tensor, J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., p. 551.
25. N. K. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, New York, 1973).
26. B. Cabral and C. Leedom, "Imaging vector fields using line integral convolution," Proc. SIGGRAPH '93 (1993), pp. 263-270.
27. A. Sundquist, "Dynamic line integral convolution for visualizing streamline evolution" IEEE Trans. Visual. Comput. Graph, (in press, 2003).
28. The only motion that is physical in this representation is the motion perpendicular to the instantaneous electric field (in electro-quasi-statics) or magnetic field (in magneto-quasi-statics). However, because of statistical correlations in the random texture used as a basis for the field representation, the Sundquist method for the calculation of the animated textures sometimes leads to apparent patterns in the texture which appear at times to move along the local field direction, as well as perpendicular to it. These apparent field aligned flows in the evolving texture patterns are artifacts of the construction process, and have no physical meaning.
29. Many of the mathematical and physical concepts in this paper are discussed at a much more detailed and sophisticated level in an expanded version of this paper available at the URL given in Ref. 7.
30. 0 Δz as the particle moves from the center of the cube to a distance Δz above the center. This is the amount of decrease in the kinetic energy of the particle as it moves upward over this same distance, as it must be.
31. Ref. 23, p. 177.
32. H. G. Schantz, "The flow of electromagnetic energy in the decay of an electric dipole," Am. J. Phys. 63, 513-520 (1995).