Investigating the magnetic interaction with GEOMAG and Tracker video analysis: static equilibrium and anharmonic dynamics

In this paper, we describe how simple experiments realizable by using easily found and low-cost materials allow students to explore quantitatively the magnetic interaction thanks to the help of an Open Source Physics tool, the Tracker Video Analysis software. The static equilibrium of a 'column' of permanents magnets is carefully investigated by working on digital photos, while the anharmonic oscillations of a magnetic bar under the action of gravity and of magnetic repulsion are analysed by using a digital video. A detailed comparison between theoretical expectations and experimental results is discussed. We discuss how the magnetic force falls off with the distance between the permanent magnets following an inverse pth power law. Static and dynamic measurements of the force and of the periods for small amplitude harmonic oscillations yield an experimental value for p ≈ 2. The dynamical system is a good example of an anharmonic oscillator. The experiments need simple and inexpensive material to be realized and address a relevant topic in the physics curriculum; thus, they appear appropriate to be used in high school and undergraduate physics courses.