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Related Experiment Video

Updated: Jun 20, 2026

Magnetic Levitation Coupled with Portable Imaging and Analysis for Disease Diagnostics

Magnetic Levitation Coupled with Portable Imaging and Analysis for Disease Diagnostics

Published on: February 19, 2017

On-axis and off-axis levitation by a rotating permanent magnet.

Hugo Schreckenberg¹, Zayneb El Omari El Alaoui¹, Guilhem Gallot²

¹Institut Polytechnique de Paris, Ecole polytechnique, Palaiseau, France.

Physical Review. E

|June 19, 2026

Summary

High-speed rotation of a tilted magnet enables stable magnetic levitation, bypassing Earnshaw's theorem. This dynamic equilibrium allows a trapped magnet to orbit, defying gravity independently.

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High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

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Published on: May 12, 2023

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Last Updated: Jun 20, 2026

Magnetic Levitation Coupled with Portable Imaging and Analysis for Disease Diagnostics

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Published on: February 19, 2017

High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

Published on: May 12, 2023

Area of Science:

Physics
Magnetism
Classical Mechanics

Background:

Earnshaw's theorem traditionally prohibits stable static levitation of permanent magnets.
Dynamic systems can overcome stability limitations imposed by static constraints.

Purpose of the Study:

To theoretically and experimentally investigate a novel magnetic levitation method using a rotating magnet.
To analyze the conditions and stability of levitation for a trapped permanent magnet.
To explain the dynamics of the levitated magnet, including off-axis motion.

Main Methods:

Theoretical modeling of the floater magnet's in-axis and off-axis motion.
Experimental study of levitation stability against rotor speed and floater parameters.
Analysis of levitation limits and extension of the dipole moment model.

Main Results:

Achieved gravity-independent magnetic levitation by rotating a tilted permanent magnet.
Identified stable conical orbits for the levitated magnet synchronized with the rotor.
Determined levitation stability conditions, including dependence on rotor speed and floater size/shape.
Observed and analyzed the lower and upper limits of stable levitation.

Conclusions:

Dynamic stabilization through high-speed rotation provides a viable method for magnetic levitation, circumventing Earnshaw's theorem.
The study elucidates the critical role of rotational speed and magnet geometry in achieving stable levitation.
An extended dipole moment model successfully explains the off-axis dynamics of the levitated magnet.