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

TL;DR

This paper combines physics and mathematics education by experimentally analyzing magnetic field oscillations using Taylor series expansion and smartphone sensors, demonstrating good agreement between theory and experiment.

Contribution

It introduces a simple, low-cost experiment integrating physics and mathematics through Taylor series analysis of magnetic fields with smartphone data.

Findings

The Taylor series accurately models magnetic field oscillations.

Smartphone magnetometers effectively capture magnetic field variations.

Theoretical and experimental data show strong agreement.

Abstract

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 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.