A quasi-static electromagnetic analysis for experiments with strong permanent magnets

TL;DR

This paper provides a quasi-static electromagnetic analysis of the experiment where a strong permanent magnet falls through a metal cylinder, offering insights useful for education and industrial applications.

Contribution

It introduces a rigorous quasi-static theoretical model for the magnet-cylinder experiment, including numerical validation and practical insights.

Findings

The magnet falls at a constant velocity due to eddy currents.

The theory accurately predicts the magnetic damping effect.

Applications include magnet grading and metal conductivity measurements.

Abstract

An electromagnetic analysis is presented for experiments with strong permanent disc magnets. The analysis is based on the well known experiment that demonstrates the effect of circulating eddy currents by dropping a strong magnet through a vertically placed metal cylinder and observing how the magnet is slowly falling through the cylinder with a constant velocity. This experiment is quite spectacular with a super strong neodymium magnet and a thick metal cylinder made of copper or aluminum. A rigorous theory for this experiment is provided based on the quasi-static approximation of the Maxwell equations, an infinitely long cylinder (no edge effects) and a homogeneous magnetization of the disc magnet. The results are useful for teachers and students in electromagnetics who wish to obtain a deeper insight into the analysis and experiments regarding this phenomenon, or with industrial applications such as the grading and calibration of strong permanent magnets or with measurements of the conductivity of various metals, etc. Several experiments and numerical computations are included to validate and to illustrate the theory.