Permanent magnet motion in a copper tube

Authors: JAROSLAV FRANEK, MARTIN SOKA

Abstract: This paper deals with the investigation of braking forces induced by eddy currents, which have effects on the permanent magnet moving at a constant speed in the direction of the conductive tube axis. The analysis is based on calculation of an action of a force between the current density, representing the magnet, and the eddy currents. The chosen solution is based on classical electrodynamics and can serve as a guide for the calculation of other cases, where braking forces are created between the moving cell, which is a source of the magnetic field, and a close conductive subject. The obtained results indicate the braking force affecting the magnet and the dependence of this force on the current. The graphical representation of the results shows that the balancing velocity of the magnet fall is inversely proportional to the quadrant of its magnetic moment. This work may be useful for experts in the area of the design of electromagnetic clutches, brakes, and actuators and for university teachers dealing with electrodynamics. Moreover, it can serve as a demonstration of a calculation of the field by vector potential, which is an appropriate quantity used for the description of magnetic fields.

Keywords: Magnet movement, eddy currents, braking forces, diffusion equation, vector potential

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