Abstract
Static dipole-dipole magnetic interaction is a classic topic discussed in electricity and magnetism text books. Its dynamic version, however, has not been reported in scientific literature. In this article, the author presents a comprehensive analysis of the latter. We consider two identical permanent cylindrical magnets. In a practical setting, we place one of the magnets at the bottom of a vertical glass tube and then drop the second magnet in the tube. For a pair of suitable permanent magnets characterized with their mass and magnetic moment we seek oscillations of the mobile magnet resulting from the unbalanced forces of the anti-parallel magnetic dipole orientation of the pair. To quantify the observed oscillations we form an equation describing the motion of the bouncing magnet. The strength of the magnet-magnet interaction is in proportion to the inverse fourth order separation distance of the magnets. Consequently, the corresponding equation of motion is a highly nonlinear differential equation. We deploy Mathematica and solve the equation numerically resulting in a family of kinematic information. We show our theoretical model with great success matches the measured data.
Highlights
It is trivial to quantify the electrostatic interaction between two point-like charges; in practice, it is challenging to deal with point-like charges
The mutual magneto static interaction force between two magnets is elevated beyond monopole-monopole interaction; it is considered as magnetic dipole-dipole interaction
As we pointed out in the introduction, the practical aspects of dynamic dipole-dipole magnetic interaction have not been discussed in scientific literature
Summary
It is trivial to quantify the electrostatic interaction between two point-like charges; in practice, it is challenging to deal with point-like charges. The planar configuration is trivialized further to a one dimensional manageable situation; magnets are aligned along their mutual common axial axis [1]. Even for this configuration to the knowledge of the author there is no report utilizing its practical dynamic application. The problem is posed: Consider two permanent magnets Position them along their mutual common axial axis and orient their magnetic moments so that are anti-parallel. We have observed the pair of our selected magnets always are subject to R<
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