Unified Approach to The Electromagnetic Field: The Role of Sources, Causality and Wave Propagation

  • Álvaro Suárez Consejo de Formación en Educación, Uruguay http://orcid.org/0000-0002-5345-5565
  • Jenaro Guisasola Donostia Physics Education Research Group (UPV/EHU), Spain
  • Arturo Martí Instituto de Física, Facultad de Ciencias, Universidad de la República, Uruguay
  • Kristina Zuza Department of Applied Physics, University of Basque Country, Spain


The question of the sources of electric and magnetic fields and their causes has been discussed extensively in the literature over the last decades. In this article, we approach this problem from the unified treatment of electromagnetic fields emphasizing the role of their sources in accordance with the cause-effect relationships. First, we analyze whether this unified treatment contributes to a better understanding of these phenomena. Then, we discuss the implications for teaching of a correct understanding of electromagnetic field sources and causality in Maxwell's equations. In particular, we present a series of examples at the introductory physics level that allow us to recognize the reasons why considering electric and magnetic fields as disjoint entities can lead to contradictions.


Alonso, M., & Finn, E. J. (1983). Fundamental University Physics, Volume Two, Fields and Waves.
Arthur, J. W. (2009). An elementary view of Maxwell's displacement current. IEEE Anten-nas and Propagation Magazine, 51(6), 58-68.
Batell, B., & Ferstl, A. (2003). Electrically induced magnetic fields; a consistent approach. American Journal of Physics, 71(9), 925-929.
Bauer, W., & Westfall, G. D. (2014). University physics with modern physics, Volume 2. McGraw Hill Education.
Berkson, W. (2014). Fields of Force: The Development of a World View from Faraday to Einstein. Routledge.
Bunge, M. (2009). Causality and modern science. New Brunswick.
Buschauer, R. (2013). Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current. The Physics Teacher, 51(9), 542-543.
Campos, E., Zavala, G., Zuza, K., & Guisasola, J. (2019). Electric field lines: The implica-tions of students' interpretation on their understanding of the concept of electric field and of the superposition principle. American Journal of Physics, 87(8), 660-667.
Campos, E., Hernandez, E., Barniol, P., & Zavala, G. (2021). Phenomenographic analysis and comparison of students’ conceptual understanding of electric and magnetic fields and the principle of superposition. Physical Review Physics Education Re-search, 17(2), 020117.
Chabay, R., & Sherwood, B. (2006). Restructuring the introductory electricity and mag-netism course. American Journal of Physics, 74(4), 329-336.
Chabay, R. W., & Sherwood, B. A. (2015). Matter and interactions. John Wiley & Sons.
Chalmers, A. F. (1975). Maxwell and the displacement current. Physics education, 10(1), 45.
Darrigol, O. (2000). Electrodynamics from Ampere to Einstein. New York: Oxford Univer-sity Press Inc.
Docktor, J. L., & Mestre, J. P. (2014). Synthesis of discipline-based education research in physics. Physical Review Special Topics-Physics Education Research, 10(2), 020119.
Fishbane, P. M., Gasiorowicz, S., & Thorton, S. T. (2005). Physics For Scientists and Engi-neers. Prentice Hall.
French, A. P. (2000). Is Maxwell’s displacement current a current? The Physics Teacher, 38(5), 274-276.
Galili, I., & Kaplan, D. (1997). Changing approach to teaching electromagnetism in a con-ceptually oriented introductory physics course. American Journal of Physics, 65(7), 657-667.
Galili, I., & Goihbarg, E. (2005). Energy transfer in electrical circuits: A qualitative account. American journal of physics, 73(2), 141-144.
Giancoli, D. C. (2008). Physics for scientists and engineers with modern physics. Pearson Education.
Griffiths, D. J., & Heald, M. A. (1991). Time‐dependent generalizations of the Biot–Savart and Coulomb laws. American Journal of Physics, 59(2), 111-117.
Griffiths, D. J. (2013). Introduction to Electrodynamics. Pearson Education.
Guisasola, J., Salinas, J., Almudí, J. M., & Velazco, S. (2003). Análisis de los Procesos de Aplicación de las Leyes de Gauss y Ampere por Estudiantes Universitarios de Es-paña y Argentina. Revista Brasileira de Ensino de Física, 25(2), 195-206.
Guisasola, J., Almudi, J. M., & Zubimendi, J. L. (2004). Difficulties in learning the introduc-tory magnetic field theory in the first years of university. Science Education, 88(3), 443-464.
Guisasola, J., Almudí, J. M., Salinas, J., Zuza, K., & Ceberio, M. (2008). The Gauss and Ampere laws: different laws but similar difficulties for student learning. European Journal of Physics, 29(5), 1005.
Heald, M. A., & Marion, J. B. (2012). Classical electromagnetic radiation. Courier Corpora-tion.
Hill, S. E. (2010). Rephrasing Faraday's law. The Physics Teacher, 48(6), 410-412.
Hill, S. E. (2011). Reanalyzing the Ampère-Maxwell Law. The Physics Teacher, 49(6), 343-345.
Jefimenko, O. D. (1989). Electricity and Magnetism: An Introduction to the Theory of Elec-tric and Magnetic Fields. Electret Scientific.
Jefimenko, O. D. (1992). Solutions of Maxwell’s equations for electric and magnetic fields in arbitrary media. American journal of physics, 60(10), 899-902.
Jefimenko, O. D. (2004). Presenting electromagnetic theory in accordance with the principle of causality. European journal of physics, 25(2), 287.
Knight, R. D. (2013). Physics for Scientists and Engineers with Modern Physics: A Strate-gic Approach. Pearson Addison Wesley.
Lea, S. M., & Burke, J. R. (1998). Physics: The Nature of Things. Brooks.
Lima, M. C. D. (2019). Sobre o surgimento das equações de Maxwell. Revista Brasileira de Ensino de Física, 41.
Maxwell, J. C. (1873). A treatise on electricity and magnetism (Vol. II). Oxford: Clarendon Press.
Maxwell, J. C. (1890). The scientific papers of James Clerk Maxwell; edited by WD Niven.
Milsom, J. A. (2020). Untold secrets of the slowly charging capacitor. American Journal of Physics, 88(3), 194-199.
Moore, T. A. (2017). Six Ideas that Shaped Physics: Electric and Magnetic Fields are Uni-fied. Unit E. McGraw-Hill Science, Engineering & Mathematics.
Ohanian, H. C., & Markert, J. T. (2007). Physics for engineers and scientists. Norton.
Rainson, S., Tranströmer, G., & Viennot, L. (1994). Students’ understanding of superposi-tion of electric fields. American Journal of Physics, 62(11), 1026-1032.
Resnick, R., Halliday, D. & Krane, K. (2003). Physics, Volume 2. John Wiley & Sons.
Rosser, W. G. V. (1963). Interpretation of the Displacement Current. American Journal of Physics, 31(10), 807-808.
Rosser, W. G. V. (1976). Does the displacement current in empty space produce a magnetic field? American Journal of Physics, 44(12), 1221-1223.
Rosser, W. G. V. (2013). Interpretation of classical electromagnetism (Vol. 78). Springer Science & Business Media.
Serway, R. A., & Jewett, J. W. (2019). Physics for scientists and engineers, Volume 2. Cen-gage learning.
Suárez, Á. (2013). El campo magnético de una carga en movimiento como ejemplo didáctico de aplicación de la corriente de desplazamiento. Lat. Am. J. Phys. Educ. Vol, 7(1), 96.
Tipler, P. A., & Mosca, G. (2007). Physics for scientists and engineers. Freeman and Com-pany.
Tran, M. (2018). Evidence for Maxwell’s equations, fields, force laws and alternative theo-ries of classical electrodynamics. European Journal of Physics, 39(6), 063001.
Young, H. D., & Freedman, R. A. (2019). University Physics with Modern Physics. Pearson Education.
Wangsness, R. K. (1979). Electromagnetic fields. New York: Wiley.
Zuza, K., Guisasola, J., Michelini, M., & Santi, L. (2012). Rethinking Faraday's law for teaching motional electromotive force. European Journal of Physics, 33(2), 397.
How to Cite
SUÁREZ, Álvaro et al. Unified Approach to The Electromagnetic Field: The Role of Sources, Causality and Wave Propagation. European Journal of Physics Education, [S.l.], v. 14, n. 2, p. 1-16, july 2023. ISSN 1309-7202. Available at: <http://www.eu-journal.org/index.php/EJPE/article/view/349>. Date accessed: 02 dec. 2023.
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