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

Abstract

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 behaviour of the interaction force at short and large 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.

Three experiments on the Einstein’s lift

“…Figure 7 shows the plots of the positions and velocity versus time of the lift and the magnet in the lab frame of reference as for the spring-ball system. Also, in this case both In the first phase of this motion, the acceleration follows a power law (here power 3.7) according to the predicted dipole-dipole interaction [14]. In the inset the velocity versus time.…”

“…The linear behaviour confirms that the ball is moving up with a uniform speed. (Right) The acceleration in the moving reference of frame versus the relative position of the ball.In the first phase of this motion, the acceleration follows a power law (here power 3.7) according to the predicted dipole-dipole interaction[14]. In the inset the velocity versus time.…”

Determining the magnetization of a permanent magnet from static equilibrium

“…The solid line is the best-fit curve. domain of validity of the model by showing the curves of the asymptotic behaviour of magnetic forces described in other work [11].…”

“…These results give experimental support to the magnetic dipole model. Moreover, whatever the length of the stack and for the whole equilibrium distances investigated [11], the model proposed in this paper is tested by its ability to provide predictions that can be verified by the experimental data. However, when the instructor inform students about the invalidity of the model for shorter equilibrium distances, and thus the total mass of the mobile system, they are surprised.…”

“…It can prevent students from running experiments in small groups. They include analysis of free oscillations of permanent magnets placed in a uniform magnetic field produced by a large coil [8] or a pair of Helmholtz coils [9]; experiments with a precision digital balance to measure the magnetic force [10,11]; experiment using a chip to make a magnetic probe connecting to a precision voltmeter for analysing the magnetic field of a magnet [12]; and experiments using complicated apparatus that are inappropriate to an educational purpose [13,14]. However, descriptions of experiments based on static equilibrium by means of a basic equipment available in all physics laboratories have not been widely considered in physics teaching literature.…”