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

• Published in: Multidisciplinary journal for education, social and technological sciences Vol. 12; no. 1; pp. 80 - 94
• Main Authors: Ortuño-Molina, S., Garmendía-Martínez, A., Fernández de Córdoba, P., Castro-Palacio, J. C., Monsoriu, J. A., Muñoz-Pérez, F. M.
• Format: Journal Article
• Language: English
• Published: Universitat Politècnica de València 01.04.2025
• Subjects: magnetic field; magnetometer; sensors; smartphone; taylor series
• ISSN: 2341-2593; 2341-2593
• DOI: 10.4995/muse.2025.22684

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.