A collection of point charges cannot be held in a stable stationary equilibrium purely by electrostatic forces alone. Proved by Samuel Earnshaw, it explains why static electric or magnetic fields alone cannot levitate a charged object without additional stabilizing forces.
Facts
StatementA collection of point charges interacting only through the classical inverse-square electrostatic force cannot be held in a stable stationary equilibrium by that force alone. Because the electrostatic potential has no local minimum in free space, any such configuration always has at least one charge that a small displacement pushes further away rather than back toward equilibrium. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Earnshaw's Theorem (Wikipedia)
Wikimedia FoundationLead section
This was first proven by British mathematician Samuel Earnshaw in 1842.
Lead section, first sentence
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges.
Lead section, second sentence
This was first proven by British mathematician Samuel Earnshaw in 1842.
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