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.
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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
Statement Form Statement Form Earnshaw's Theorem
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Source Wikipedia: Samuel Earnshaw
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Source Earnshaw's Theorem (Wikipedia)
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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.
In Group: Electromagnetism, Optics and Continuum Mechanics, Lead
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.
Proved By: Samuel Earnshaw, Lead
This was first proven by British mathematician Samuel Earnshaw in 1842.
View the Source Wikipedia: Samuel Earnshaw
Principal Result Of: Samuel Earnshaw, Article textQuote, Principal Result Of: Samuel Earnshaw, Article text
Samuel Earnshaw (1 February 1805, Sheffield, Yorkshire, 6 December 1888, Sheffield, Yorkshire) was an English clergyman and mathematician and physicist, noted for his contributions to theoretical physics, especially for proving Earnshaw's theorem.
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