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Learning difficulties among students when applying Ampére-Maxwell’s law and its implications for teaching

Álvaro Suárez

Arturo C. Marti

Kristina Zuza

Jenaro Guisasola

  • Departamento de Física, Consejo de Formación en Educación, Montevideo, Uruguay

  • Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, Montevideo, 11200, Uruguay

  • Department of Applied Physics and Donostia Physics Education Research Group, University of the Basque Country (UPV/EHU), San Sebastian 20018, Spain

  • Donostia Physics Education Research Group, University of the Basque Country (UPV/EHU), San Sebastian 20018, Spain and School of Dual Engineering, Institute of Machine Tools (IMH), Elgoibar, Spain

Phys. Rev. Phys. Educ. Res. 20, 010143 – Published 16 May, 2024

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.20.010143

Abstract

We investigate learning difficulties among second-year students in electromagnetism courses when they apply Ampère-Maxwell’s law. Using phenomenography, we analyzed written answers from 65 undergraduate physics students to four questions on Ampère’s and Ampère-Maxwell’s laws. We complemented our research by interviewing 12 students. To design the questionnaire, we ran an epistemological analysis of classical electromagnetism which helped us to identify a set of key essential concepts to understand this theory, guided the definition of learning objectives, and drew up the questions. The results revealed that the students found it hard to recognize the validity framework from Ampère’s law and to apply Ampère-Maxwell’s law. They face particular difficulties to recognize the appearance of the displacement current and the relationship between the circulation of the magnetic field and an electric field that is variable over time.

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References (75)

  1. R. E. Pepper, S. V. Chasteen, S. J. Pollock, and K. K. Perkins, Our best juniors still struggle with Gauss’s law: Characterizing their difficulties, AIP Conf. Proc. 1289, 245 (2010).
  2. R. E. Pepper, S. V. Chasteen, S. J. Pollock, and K. K. Perkins, Observations on student difficulties with mathematics in upper-division electricity and magnetism, Phys. Rev. ST Phys. Educ. Res. 8, 010111 (2012).
  3. J. Guisasola, J. Salinas, J. M. Almudí, and S. Velazco, Análisis de los procesos de aplicación de las Leyes de Gauss y Ampère por estudiantes universitarios de Espańa y Argentina, Rev. Bras. Ensino Fís. 25, 195 (2003).
  4. J. Guisasola, J. M. Almudí, J. Salinas, K. Zuza, and M. Ceberio, The Gauss and Ampere laws: Different laws but similar difficulties for student learning, Eur. J. Phys. 29, 1005 (2008).
  5. E. Campos, E. Hernandez, P. Barniol, and G. Zavala, Analysis and comparison of students’ conceptual understanding of symmetry arguments in Gauss’s and Ampere’s laws, Phys. Rev. Phys. Educ. Res. 19, 010103 (2023).
  6. C. Singh, Student understanding of symmetry and Gauss’s law of electricity, Am. J. Phys. 74, 923 (2006).
  7. J. Li and C. Singh, Investigating and improving introductory physics students’ understanding of symmetry and Gauss’s law, Eur. J. Phys. 39, 015702 (2017).
  8. Ş. Atasoy, Effect of writing-to-learn strategy on undergraduates’ conceptual understanding of electrostatics, Asia-Pac. Educ. Researcher 22, 593 (2013).
  9. C. S. Wallace and S. V. Chasteen, Upper-division students’ difficulties with ampère’s law, Phys. Rev. ST Phys. Educ. Res. 6, 020115 (2010).
  10. E. Hernandez, E. Campos, P. Barniol, and G. Zavala, Students’ conceptual understanding of electric flux and magnetic circulation, Phys. Rev. Phys. Educ. Res. 19, 013102 (2023).
  11. M. Saarelainen, A. Laaksonen, and P. E. Hirvonen, Students’ initial knowledge of electric and magnetic fields—more profound explanations and reasoning models for undesired conceptions, Eur. J. Phys. 28, 51 (2006).
  12. W. M. Thong and R. Gunstone, Some student conceptions of electromagnetic induction, Res. Sci. Educ. 38, 31 (2008).
  13. J. M. A. Jenaro Guisasola and K. Zuza, University students’ understanding of electromagnetic induction, Int. J. Sci. Educ. 35, 2692 (2013).
  14. K. Zuza, J. Guisasola, M. Michelini, and L. Santi, Rethinking faraday’s law for teaching motional electromotive force, Eur. J. Phys. 33, 397 (2012).
  15. E. Bagno and B.-S. Eylon, From problem solving to a knowledge structure: An example from the domain of electromagnetism, Am. J. Phys. 65, 726 (1997).
  16. M. C. Pocoví and E. Hoyos, Corriente de desplazamiento: su presentación en textos y su comprensión por parte de los estudiantes, Enseñanza Cienc. 29, 275 (2011).
  17. A. Suárez, A. C. Martí, K. Zuza, and J. Guisasola, Electromagnetic field presented in introductory physics textbooks and consequences for its teaching, Phys. Rev. Phys. Educ. Res. 19, 020113 (2023).
  18. N. Gauthier, Displacement current, transport current, and charge conservation, Am. J. Phys. 51, 168 (1983).
  19. G. Reich, An alternative introduction to Maxwell’s displacement current, Phys. Teach. 51, 485 (2013).
  20. R. Karam, D. Coimbra, and M. Pietrocola, Comparing teaching approaches about Maxwell’s displacement current, Sci. Educ. 23, 1637 (2014).
  21. A. S. Moreno, O. J. Gómez, and J. R. A. Terrats, La enseñanza basada en preguntas: La ley de ampère y el término de maxwell, Didáct. Cienc. Exp. Soc. 38, 115 (2020).
  22. J. A. Milsom, Untold secrets of the slowly charging capacitor, Am. J. Phys. 88, 194 (2020).
  23. C. E. Mungan, Surface currents on the plates of a charging capacitor, Phys. Teach. 59, 86 (2021).
  24. H. S. Zapolsky, Does charge conservation imply the displacement current?, Am. J. Phys. 55, 1140 (1987).
  25. A. M. Wolsky, On a charge conserving alternative to Maxwell’s displacement current, Eur. J. Phys. 36, 035019 (2015).
  26. O. D. Jefimenko, Presenting electromagnetic theory in accordance with the principle of causality, Eur. J. Phys. 25, 287 (2004).
  27. S. E. Hill, Reanalyzing the Ampère-Maxwell law, Phys. Teach. 49, 343 (2011).
  28. T. A. Weber and D. J. Macomb, On the equivalence of the laws of Biot–Savart and Ampere, Am. J. Phys. 57, 57 (1989).
  29. R. Buschauer, Derivation of the Biot-Savart law from Ampere’s law using the displacement current, Phys. Teach. 51, 542 (2013).
  30. W. G. V. Rosser, Does the displacement current in empty space produce a magnetic field?, Am. J. Phys. 44, 1221 (1976).
  31. J. Roche, The present status of Maxwell’s displacement current, Eur. J. Phys. 19, 155 (1998).
  32. J. D. Jackson, Maxwell’s displacement current revisited, Eur. J. Phys. 20, 495 (1999).
  33. A. P. French, Is Maxwell’s displacement current a current?, Phys. Teach. 38, 274 (2000).
  34. J. A. Heras, A formal interpretation of the displacement current and the instantaneous formulation of Maxwell’s equations, Am. J. Phys. 79, 409 (2011).
  35. M. Landini, About the physical reality of “Maxwell’s displacement current” in classical electrodynamics, Prog. Electromagn. Res. 144, 329 (2014).
  36. T. Hyodo, Maxwell’s displacement current and the magnetic field between capacitor electrodes, Eur. J. Phys. 43, 065202 (2022).
  37. W. Berkson, Fields of Force: The Development of a World View from Faraday to Einstein (Routledge, London, 2014).
  38. O. Darrigol, Electrodynamics from Ampere to Einstein (Oxford University Press, New York, 2000).
  39. A. M. Bork, Maxwell, displacement current, and symmetry, Am. J. Phys. 31, 854 (1963).
  40. J. C. Maxwell, The Scientific Papers of James Clerk Maxwell, edited by W. D. Niven, Cambridge Library Collection—Physical Sciences Vol. 1 (Cambridge University Press, Cambridge, England, 2011).
  41. N. J. Nersessian, Faraday to Einstein: Constructing Meaning in Scientific Theories (Springer Science & Business Media, Dordrecht, 2012), Vol. 1.
  42. P. M. Harman and P. M. Harman, Energy, Force and Matter: The Conceptual Development of Nineteenth-Century Physics (Cambridge University Press, Cambridge, England, 1982).
  43. A. F. Chalmers, Maxwell and the displacement current, Phys. Educ. 10, 45 (1975).
  44. J. W. Arthur, An elementary view of Maxwell’s displacement current, IEEE Antennas Propag. Mag. 51, 58 (2009).
  45. J. C. Maxwell, A Treatise on Electricity and Magnetism (Clarendon Press, Oxford, 1881), Vol. 2.
  46. F. Marton, Phenomenography—describing conceptions of the world around us, Instr. Sci. 10, 177 (1981).
  47. P. A. Tipler and G. Mosca, Physics for Scientists and Engineers (W.H. Freeman and Company, San Francisco, 2008).
  48. H. D. Young and R. A. Freedman, University Physics with Modern Physics (Pearson Education, New York, 2020).
  49. J. Guisasola, K. Zuza, J. Ametller, and J. Gutierrez-Berraondo, Evaluating and redesigning teaching learning sequences at the introductory physics level, Phys. Rev. Phys. Educ. Res. 13, 020139 (2017).
  50. K. Zuza, P. Sarriugarte, J. Ametller, P. R. L. Heron, and J. Guisasola, Towards a research program in designing and evaluating teaching materials: An example from dc resistive circuits in introductory physics, Phys. Rev. Phys. Educ. Res. 16, 020149 (2020).
  51. J. Guisasola, J. Ametller, and K. Zuza, Investigación basada en el diseño de secuencias de Enseñanza-Aprendizaje: una línea de investigación emergente en Enseñanza de las Ciencias, Rev. Eureka Enseñanza Divulgación Cienc. 18, 1801 (2021).
  52. J. Guisasola, K. Zuza, P. Sarriugarte, and J. Ametller, Research-based teaching-learning sequences in physics education: A rising line of research, in The International Handbook of Physics Education Research: Special Topics (AIP Publishing LLC, Melville, NY, 2023).
  53. L. Cohen, L. Manion, and K. Morrison, Research Methods in Education (Taylor & Francis Group, London, 2007), Chap. 4.
  54. H. E. Gardner, The Unschooled Mind: How Children Think and How Schools Should Teach (Basic books, New York, 2011).
  55. J. Guisasola, E. Campos, K. Zuza, and G. Zavala, Phenomenographic approach to understanding students’ learning in physics education, Phys. Rev. Phys. Educ. Res. 19, 020602 (2023).
  56. F. Marton and S. Booth, Learning and Awareness (Routledge, London, 2013).
  57. M. Banerjee, M. Capozzoli, L. McSweeney, and D. Sinha, Beyond kappa: A review of interrater agreement measures, Can. J. Stat. 27, 3 (1999).
  58. V. K. Otero and D. B. Harlow, Getting Started in Qualitative Physics Education Research, Reviews in PER Vol. 2 (2009).
  59. M. G. M. Ferguson-Hessler and T. de Jong, On the quality of knowledge in the field of electricity and magnetism, Am. J. Phys. 55, 492 (1987).
  60. M. T. Chi, M. Bassok, M. W. Lewis, P. Reimann, and R. Glaser, Self-explanations: How students study and use examples in learning to solve problems, Cogn. Sci. 13, 145 (1989).
  61. L. Viennot, Raisonner en physique: La part du sens commun (De Boeck, Louvain la Neuve, 1996).
  62. F. Halbwachs, Réflexions sur la causalité physique, in Les théories de la causalité, edited by M. Bunge, F. Halbwachs, T. S. Kuhn, and J. Piaget (Presses Universitaires de France, Paris, 1971), pp. 19–36.
  63. A. Leniz, K. Zuza, and J. Guisasola, Students’ reasoning when tackling electric field and potential in explanation of dc resistive circuits, Phys. Rev. Phys. Educ. Res. 13, 010128 (2017).
  64. J. Walker, R. Resnick, and D. Halliday, Halliday and Resnick Fundamentals of Physics (Wiley, New York, 2014).
  65. J. Guisasola, J. M. Almudí, and J. L. Zubimendi, Difficulties in learning the introductory magnetic field theory in the first years of university, Sci. Educ. 88, 443 (2004).
  66. D. E. Trowbridge and L. C. McDermott, Investigation of student understanding of the concept of velocity in one dimension, Am. J. Phys. 48, 1020 (1980).
  67. D. E. Trowbridge and L. C. McDermott, Investigation of student understanding of the concept of acceleration in one dimension, Am. J. Phys. 49, 242 (1981).
  68. L. D. Allen, An Investigation into Student Understanding of Magnetic Induction (The Ohio State University, Columbus, OH, 2001).
  69. A. F. Heckler and E. C. Sayre, What happens between pre- and post-tests: Multiple measurements of student understanding during an introductory physics course, Am. J. Phys. 78, 768 (2010).
  70. M. H. P. Kesonen, M. A. Asikainen, and P. E. Hirvonen, University students’ conceptions of the electric and magnetic fields and their interrelationships, Eur. J. Phys. 32, 521 (2011).
  71. M. Leclerc, Hall effect probe and Ampere’s law, Am. J. Phys. 56, 954 (1988).
  72. S. Frish and A. Timoreva, General Physics Course (Mir, Moscow, 1957).
  73. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics. Vol. II (Addison-Wesley Publishing Company, Boston, MA, 1963), Chap. 18.
  74. A. Suárez, A. C. Martí, K. Zuza, and J. Guisasola, Las relaciones causa-efecto en las ecuaciones de Maxwell y sus implicancias en la enseñanza del electromagnetismo en los cursos introductorios de física, Rev. Bras. Ensino Fís. 44, e20220230 (2022).
  75. Álvaro Suárez, J. Guisasola, A. Martí, and K. Zuza, Unified approach to the electromagnetic field: The role of sources, causality and wave propagation, Eur. J. Phys. Educ. 14, 1 (2023), https://www.eu-journal.org/index.php/EJPE/article/view/349.

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