Exploring magnetic interactions between magnets and a magnetizable alloy

Abstract

Traditional problems in mechanics usually involve forces that generate motions described by analytical solutions, easily obtained from differential equations. However, when magnetic forces are involved, problems can be very complex to describe analytically. In this paper, we describe the problematic situation of magnets that attract a coin of a magnetizable alloy. The experiment was filmed with a camera at a high rate frame. A Coulomb-type model inversely proportional to the square of the distance between the magnets and the coin was tested to fit the experimental results, without much success. The problem was then solved analytically, assuming that the force exerted on the coin varies exponentially with the distance between them. The experimental data were compared with those predicted by the theoretical model. The results confirm that the theoretical model is the most adequate to describe the kind of interaction involved, showing that this interaction is very different from that usually found in problems with gravitational, electrical or elastic forces. This work opens up future perspectives for investigations with attractive and repulsive forces between magnets.