Ampère currents versus magnetization charges: the theory behind Experimental Problem #2 at the 41st International Physics Olympiad

Abstract

We analyze theoretically the interaction between a bar magnet and a magnetic ring, as proposed in Experimental Problem #2 at the 41st International Physics Olympiad. The ring is modeled with Ampère currents circulating along its inner and outer circumferences. The bar magnet is represented by two point magnetization charges situated on the ends of the bar. A simple graphical analysis is proposed, which allows one to predict the number, the coordinates, and the stability of the equilibrium positions of the bar magnet. The calculated distance-force dependence is in excellent agreement with the experimental data. We confirm further the validity of our approach by performing experiments with bar magnets of different lengths.