We present a comparative investigation of two-dimensional tractor magnet configurations, analyzing both theoretical predictions and experimental results with a focus on the minimal tractor magnet. The minimal tractor magnet consists of a rigid assembly of one attracting magnet (attractor), two repelling magnets (repulsors), and a fourth magnet (follower) that is magnetically stabilized in a local energy minimum. The theoretical framework relies on magnetostatics and stability analysis of stationary equilibria. To calculate the magnetostatic force and energy, we use a multipole method. In a first approximation, we derive analytical results from the point dipole approximation. The point dipole analysis defines an upper bound criterion for the magnetic moment ratio and provides analytical expressions for stability bounds in relation to geometry parameters. Our experimental results are consistent with the predictions from the fourth-order multipole expansion. Beyond the minimal tractor magnet, we introduce a more advanced configuration that allows for a higher magnetic binding energy and follower capture at larger distances.
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Understanding two-dimensional tractor magnets: Theory and realizations
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August 2024
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August 01 2024
Understanding two-dimensional tractor magnets: Theory and realizations
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Michael P. Adams
Michael P. Adams
a)
Department of Physics and Materials Science, University of Luxembourg
, 162A avenue de la Faiencerie, L-1511 Luxembourg, Grand Duchy of Luxembourg
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Michael P. Adams
a)
Department of Physics and Materials Science, University of Luxembourg
, 162A avenue de la Faiencerie, L-1511 Luxembourg, Grand Duchy of Luxembourg
a)
Electronic mail: [email protected], ORCID: 0000-0001-9269-8087.
Am. J. Phys. 92, 576–582 (2024)
Article history
Received:
January 17 2024
Accepted:
May 08 2024
Citation
Michael P. Adams; Understanding two-dimensional tractor magnets: Theory and realizations. Am. J. Phys. 1 August 2024; 92 (8): 576–582. https://doi.org/10.1119/5.0198262
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