Stable Levitation

Earnshaw's Theorem, formulated by Samuel Earnshaw, serves as a foundational principle within classical mechanics (Simon et al. in Am J Phys 69:702–713, 2001; Geim et al. in Nature 400:323–324, 1999), positing the impossibility of point particles achieving stable equilibrium solely under classical inverse square law forces. This theorem resonates throughout the realms of physics, rendering stable suspension unattainable through gravity, electrostatics, and static magnetism. At its core lies the interplay of electric field line divergence and Gauss’s law, resulting in the absence of stable equilibria in open spaces. The electric force derived from potential adheres mathematically to Laplace’s equation, a perpetually divergence-free framework.