Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

Science and Education

Volumn 20, Issue 7, 2011, Pages 687-700

  Tweney, Ryan D ^a,b  

^a BOWLING GREEN STATE UNIVERSITY   (United States)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79959542348     PISSN: 09267220     EISSN: 15731901     Source Type: Journal    
DOI: 10.1007/s11191-010-9256-9     Document Type: Article

References (47)

1. Anzai, Y. (1991). Learning and use of representations for physics expertise. In K. A. Ericsson & J. Smith (Eds.), Toward a general theory of expertise: Prospects and limits (pp. 64-92). New York: Cambridge University Press.
2. Buchwald, J. Z. (1985). From Maxwell to microphysics: Aspects of electromagnetic theory in the last quarter of the Nineteenth Century. Chicago: University of Chicago Press.
3. Campbell, L., & Garnett, W. (1882). The life of James Clerk Maxwell, with a selection from his correspondence and occasional writings and a sketch of his contributions to science. London: Macmillan and Co.
4. Chase, W. G., & Simon, H. A. (1973). The mind's eye in chess. In W. G. Chase (Ed.), Visual information processing (pp. 215-281). New York: Academic Press.
5. Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152.
6. Clement, J. (2008). Creative model construction in scientists and students: Imagery, analogy, and mental simulation. Dordrecht: Springer.
7. Clement, J. C., & Steinberg, M. S. (2002). Step-wise evolution of models of electric circuits: A 'learning aloud' case study. Journal of the Learning Sciences, 11(4), 380-452.
8. Craik, A. D. D. (2008). Mr. Hopkins' men: Cambridge reform and British mathematics in the 19th century. London: Springer.
9. Darrigol, O. (2000). Electrodynamics from Ampère to Einstein. Oxford: Oxford University Press.
10. Dyson, F. J. (1999). Why is Maxwell's theory so hard to understand? In James Clerk Maxwell Foundation (Ed.), James Clerk Maxwell commemorative booklet (pp. 9-14). Edinburgh: James Clerk Maxwell Foundation.
11. Einstein, A., & Infeld, L. (1938). The evolution of physics: From early concepts to relativity and quanta. New York: Simon and Schuster.
12. Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245.
13. Ericsson, K. A., Charness, N., Feltovich, P. J., & Hoffman, R. R. (Eds.). (2006). The Cambridge handbook of expertise and expert performance. New York: Cambridge University press.
14. Faraday, M. (Ed.) (1839-1855). Experimental researches in electricity (3 Vols.). London: Taylor and Francis.
15. Faraday, M. (1846). Experimental researches in electricity. 19th series. On the magnetization of light and the illumination of magnetic lines of force. In M. Faraday (Ed.) (1855), Experimental researches in electricity (Vol. 3, pp. 1-26). London: Taylor and Francis.
16. Faraday, M. (1852). On the physical character of the lines of magnetic force. Reprinted in M. Faraday (Ed.) (1855), Experimental researches in electricity (Vol. 3, pp. 407-437). London: Taylor and Francis.
17. Feynman, R. P., Gottlieb, M. A., & Leighton, R. (1961/2006). Feynman's tips on physics. San Francisco, CA: Pearson/Addison Wesley. (Lectures first given in 1961).
18. Frost, P. (1854). Newton's Principia. Sections I. II. III. With notes and illustrations. Also a collection of problems principally intended as examples of Newton's methods. Cambridge: Macmillan and Co.
19. Gooding, D. C. (1981). Final steps to the field theory: Faraday's study of magnetic phenomena. Historical Studies in the Physical Sciences, 11, 231-275.
20. Gooding, D. C. (1992). Mathematics and method in Faraday's experiments. Physis, 29 (New Series), 121-147.
21. Gooding, D. C. (2005). Seeing the forest for the trees: Visualization, cognition, and scientific inference. In M. E. Gorman, R. D. Tweney, D. C. Gooding, & A. P. Kincannon (Eds.), Scientific and technological thinking (pp. 173-218). Mahwah, NJ: Lawrence Erlbaum.
22. Harman, P. M. (1985). Edinburgh philosophy and Cambridge physics: The natural philosophy of James Clerk Maxwell. In P. M. Harman (Ed.), Wranglers and physicists: Studies on Cambridge mathematical physics in the nineteenth century (pp. 202-224). Manchester: Manchester University Press.
23. Harman, P. M. (Ed.). (1990). The scientific letters and papers of James Clerk Maxwell. (Vol. I., 1846-1862). Cambridge: Cambridge University press.
24. Harman, P. M. (1998). The natural philosophy of James Clerk Maxwell. Cambridge: Cambridge University Press.
25. Hunt, B. R. (1991). The Maxwellians. Ithaca, NY: Cornell University Press.
26. Ippolito, M. F., & Tweney, R. D. (1995). The inception of insight. In R. J. Sternberg & J. E. Davidson (Eds.), The nature of insight (pp. 433-462). Cambridge, MA: The MIT Press.
27. James, F. A. J. L. (1998). Faraday, Maxwell, and field theory. In F. A. J. L. James (Ed.), Semaphores to short waves (pp. 71-84). London: Royal Society for the Encouragement of Arts and Manufactures.
28. Klahr, D. (2000). Exploring science: The cognition and development of discovery processes. Cambridge, MA: MIT Press.
29. Kurz, E. M., & Tweney, R. D. (1998). The practice of mathematics and science: From calculus to the clothesline problem. In M. Oaksford & N. Chater (Eds.), Rational models of cognition (pp. 415-438). Oxford: Oxford University Press.
30. Langley, P., Simon, H. A., Bradshaw, G. L., & Zytkow, J. M. (1987). Scientific discovery: Computational explorations of the discovery process. Cambridge, MA: MIT Press.
31. Main, I. G. (1984). Vibrations and waves in physics (2nd ed.). Cambridge: Cambridge University Press.
32. Maxwell, J. C. (1846). On the description of oval curves, and those having a plurality of foci. Reprinted in W. D. Niven (Ed.) (1890), The scientific papers of James Clerk Maxwell (Vol. 1, pp. 1-3). Cambridge: Cambridge University Press.
33. Maxwell, J. C. (1855-1856). On Faraday's lines of force. Reprinted in W. D. Niven (Ed.) (1890), The scientific papers of James Clerk Maxwell (Vol. 1, pp. 155-229). Cambridge: Cambridge University Press.
34. Maxwell, J. C. (1861-1862). On physical lines of force. Reprinted in W. D. Niven (Ed.) (1890), The scientific papers of James Clerk Maxwell (Vol. 1, pp. 451-513). Cambridge: Cambridge University Press.
35. Maxwell, J. C. (1864). A dynamical theory of the electromagnetic field. Reprinted in W. D. Niven (Ed.) (1890), The scientific papers of James Clerk Maxwell (Vol. 1, pp. 526-597). Cambridge: Cambridge University Press.
36. Maxwell, J. C. (1873/1891). A treatise on electricity and magnetism (2 Vols.). Oxford: Clarendon Press. (Third edition, revised by J. J. Thompson).
37. Nersessian, N. J. (2002). Maxwell and the 'method of physical analogy': Model-based reasoning, generic abstraction, and conceptual change. In D. B. Malament (Ed.), Reading natural philosophy: Essays in the history and philosophy of science and mathematics (pp. 129-166). Chicago: Open Court.
38. Nersessian, N. J. (2008). Creating scientific concepts. Cambridge, MA: MIT Press.
39. Siegel, D. M. (1991). Innovation in Maxwell's electromagnetic theory: Molecular vortices, displacement current, and light. Cambridge: Cambridge University Press.
40. Simpson, T. K. (1997). Maxwell on the electromagnetic field: A guided study. New Brunswick, NJ: Rutgers University Press.
41. Simpson, T. K. (2005). Figures of thought: A literary appreciation of Maxwell's Treatise on electricity and magnetism. Santa Fe, NM: Green Lion Press.
42. Steinberg, M. S. (2008). Applying modeling theory to curriculum development: From electric circuits to electromagnetic fields. In J. J. Clement & M. A. Rea-Ramirez (Eds.), Model based learning and instruction in science (pp. 151-171). Dordrecht: Springer.
43. Steinberg, M. S., & Wainwright, C. L. (1993). Using models to teach electricity-the CASTLE project. Physics Teacher, 31, 353-357.
44. Tweney, R. D. (1992). Inventing the field: Michael Faraday and the creative 'engineering' of electromagnetic field theory. In R. J. Weber & D. N. Perkins (Eds.), Inventive minds: Creativity in technology (pp. 31-47). Oxford: Oxford University Press.
45. Tweney, R. D. (2001). Scientific thinking: A cognitive-historical approach. In K. Crowley, C. D. Schunn, & T. Okada (Eds.), Designing for science: Implications from everyday, classroom, and professional settings (pp. 141-173). Mawah, NJ: Erlbaum.
46. Tweney, R. D. (2009). Mathematical representations in science: A cognitive-historical case study. Topics in Cognitive Science, 1, 758-776.
47. Warwick, A. (2003). Masters of theory: Cambridge and the rise of mathematical physics. Chicago: University of Chicago Press.