How the Levitron levitates a spinning top

Settled in 1996 by Michael Berry.

The Levitron, a spinning magnetic top that hovers above a magnetized base, was patented by Roy Harrigan in the early 1980s, and its stability initially seemed to violate Earnshaw's theorem, which proves no static configuration of magnets can be in stable equilibrium. In 1996 mathematical physicist Michael Berry showed that the top's rapid spin is essential: because the top precesses, its magnetic moment adiabatically tracks the local field direction, creating an effective potential well that sidesteps Earnshaw's static-equilibrium restriction. This explained both why the top must be spun within a narrow speed range and why it eventually falls once friction slows the spin below a critical threshold.

A children's toy top hovering in midair looks like it breaks a 19th-century theorem of electromagnetism, but it actually reveals a subtle adiabatic-invariance trick hiding in plain sight in classical mechanics.

Explanations that circulated

• A naive reading of Earnshaw's theorem (no static arrangement of magnets can be in stable equilibrium) is sometimes taken to mean the Levitron must involve hidden trickery; it works precisely because the top is spinning, not static - Earnshaw's theorem does not apply to this dynamic, adiabatically-varying spin system.
• Some popular descriptions attribute the levitation to simple magnetic repulsion balancing gravity without explaining why that balance is stable - the real stabilizing mechanism is adiabatic following of the spin axis to the local field direction as the top slowly precesses.

References

• The Levitron: an adiabatic trap for spins, M. V. Berry, Proceedings of the Royal Society A, 1996