Combining Physics and Mathematics Learning: A Taylor Series Analysis of an Oscillating Magnetic Field

• Ortuño-Molina, S. ^[1] ; Garmendía-Martínez, A. ^[1] ; Fernández de Córdoba, P. ^[1] ; Castro-Palacio, J. C. ^[1] ; Monsoriu, J. A. ^[1] ; Muñoz-Pérez, F. M. ^[1]
  1. [1] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
• Localización: Multidisciplinary Journal for Education, Social and Technological Sciences, ISSN-e 2341-2593, Vol. 12, Nº. 1, 2025, 94 págs.
• Idioma: inglés
• DOI: 10.4995/muse.2025.22684
• Enlaces
  • Texto completo
• Resumen

  • In this work, we present a simple and low-cost experiment designed to study the oscillations of the magnetic field created by a cylindrical magnet under two different conditions: far and short distances from the magnetic sensor. A Taylor’s series expansion of the magnetic field function has been done to study the convergence of the polynomial series to the real field in both situations. To carry out the experiment, a small cylindrical magnet has been attached to an oscillating and well-known spring-mass system. The resulting oscillating magnetic field has been registered with the smartphone by using the magnetometer sensor. A very good agreement has been obtained between the theoretical model for the magnetic field and the experimental data collected with the sensor located near and far from a cylindrical magnet and along its longitudinal axis.

• Referencias bibliográficas
  • Arribas, E., Escobar, I., Suarez, C. P., Najera, A., & Beléndez, A. (2015). Measurement of the magnetic field of small magnets with a...
  • Bissell, J. J. (2023). Proof of the small angle approximation sin θ ≈ θ using the geometry and motion of a simple pendulum. Int. J. Math....
  • Castro-Palacio, J.C., Velazquez-Abad, L., Gimenez, F. and Monsoriu, J.A. (2013a). Using a mobile phone acceleration sensor in physics experiments...
  • Castro-Palacio, J.C., Velazquez-Abad, L., Gimenez, F. and Monsoriu, J.A. (2013b). A quantitative analysis of coupled oscillations using mobile...
  • Dumrongkitpakorn P., Khemmani S., Plaipichit S., Wicharn S., & Puttharugsa C. (2023). Measuring the average velocity and acceleration...
  • Erol M., & Kara, A. (2023). Mathematical Modeling and Teaching of Outer Magnetic Field of a Solenoid Using Smartphones. Phys. Educ., The,...
  • Giménez, M.H., Salinas, I. and Monsoriu, J.A. (2017). Direct Visualization of Mechanical Beats by means of an Oscillating Smartphone. The...
  • Gómez-Tejedor, J.A., Castro-Palacio, J.C. and Monsoriu, J.A. (2014). The acoustic Doppler effect applied to the study of linear motions. Introduction...
  • Hochberg K., Kuhn J., & Müller A. (2018). Using smartphones as experimental tools-effects on interest, curiosity, and learning in physics...
  • Kuhn, J. and Vogt, P. (2013a). Analyzing acoustic phenomena with a smartphone microphone. The Physics Teacher 51, 118-119. https://doi.org/10.1119/1.4775539
  • Kuhn, J. and Vogt, P. (2013b). Applications and examples of experiments with mobile phones and smartphones in physics lessons. Frontiers in...
  • Kuhn, S., and Vogt, M. (Eds.). (2018). Smartphones as mobile minilabs in physics. Springer.
  • Listiaji, P., Wulandari T.D., & Putri A.A. (2023). Application of the Oscillation Concept: Measuring the Human Respiration Rate in Various...
  • Marín-Sepúlveda, C., Ortuño-Molina, S., Castro-Palacio, J.C. and Monsoriu, J.A. (2024). Acoustic testing of the inverse-square law using the...
  • Monteiro, M., Cabeza, C., & Martí, A. C. (2014). Angular velocity and centripetal acceleration relationship. The Physics Teacher, 52(6),...
  • Monteiro M., Stari C., Cabeza C., & Martí A.C. (2017). Magnetic field 'flyby' measurement using a smartphone's magnetometer...
  • Ogawara Y., Bahri S., & Mahrley S. (2017). Observation of the magnetic field using a smartphone, Phys. Teach., 55, 184-185. https://doi.org/10.1119/1.4976667
  • Parolin, S.O. and Pezzi, G. (2013). Smartphone-aided measurements of the speed of sound in different gaseous mixtures. Phys. Teach., 51, 508-509....
  • Polak, R.D., Fudala, N., Rothchild, J.T., Weiss, S.E. and Zelek, M. (2016). Easily accessible experiments demonstrating interference. Phys....
  • Riley, K. F., Hobson, M. P., & Bence, S. J. (2006). Mathematical methods for physics and engineering (3rd Edition). Cambridge University...
  • Salinas, I., Giménez, M.H., Monsoriu, J.A. and Castro- Palacio, J.C. (2018a). Characterization of linear light sources with the smartphone's...
  • Salinas, I. Giménez, M.H., Monsoriu, J.A. and Castro- Palacio, J.C. (2018b). El smartphone como barómetro en experimentos de Física. Mod....
  • Sans J.A., Manjón, F.J., Pereira A.L.J., Gomez-Tejedor, J.A. and Monsoriu, J.A. (2013). Oscillations studied with the smartphone ambient light...
  • Shakur, A. and Sinatra, T. (2013). Angular momentum. Phys. Teach., 51, 564-565. https://doi.org/10.1119/1.4830076
  • Staacks S., Hütz S., Heinke H., & Stampfer C. (2018). Advanced tools for smartphone-based experiments: phyphox. Phys Educ., 53(4), 045009....
  • Torriente-García, I., Muñoz, F.M., Castro-Palacio, J.C. and Monsoriu, J.A. (2023). RLC series circuit made simple and portable with smartphones....
  • Vieryas, (2020) Physics toolbox URL https://www.vieyrasoftware.net/ (accessed on 21-08- 2024).
  • Vogt, P., Kuhn J., (2022). Analyzing free fall with a smartphone acceleration sensor. Phys. Teach., 50, 182-183. https://doi.org/10.1088/1361-6552/ad04fb
  • Vogt, P., Kuhn J., (2022). Analyzing simple pendulum phenomena with a smartphone acceleration sensor. Phys. Teach., 50, 439- 440. https://doi.org/10.1119/1.4752056
  • Wannous, J. & Horvath, P. (2023). Precise measurements using a smartphone's magnetometer. Measuring magnetic fields and permeability....
  • Westermann, N., Staacs S., Heinke H., & Möhrke P. (2022). Measuring the magnetic field of a low frequency LC-circuit with phyphox. Phys....