Experiments and models about the force between permanent magnets: Asymptotic analysis of a difficult problem

We propose a simple experiment, which allows students to explore quantitatively the magnetic interaction between neodymium cylindrical magnets. The experiment employs a precision digital balance, two screws with known thread pitch and two transparent tubes to measure the repulsive force between two magnets as a function of their distance. Different measurements are performed, focusing on the behavior of the interaction force at short and long distances and the role of the magnets' aspect ratio. We discuss the comparison between theoretical expectations resulting from conceptually simple approximate models and experimental results. The experiments employ inexpensive materials and address a relevant topic in the physics curriculum. Thus, they are appropriate for the undergraduate physics laboratory, for advanced high school students, and in the context of teacher education and in-service training to enhance students' knowledge of magnetism.