Editing Earnshaw's theorem (section)

{{short description|Statement on equilibrium in electromagnetism}}{{More citations needed|date=February 2021}}{{Electromagnetism}}
'''Earnshaw's theorem''' states that a collection of [[point charge]]s cannot be maintained in a stable stationary [[mechanical equilibrium|equilibrium]] configuration solely by the [[electrostatic]] interaction of the charges. This was first proven by British mathematician [[Samuel Earnshaw]] in 1842.
It is usually cited in reference to [[magnetic field]]s, but was first applied to [[electrostatic field]].

Earnshaw's theorem applies to classical [[inverse-square law]] [[force]]s (electric and [[gravitational force|gravitational]]) and also to the magnetic forces of [[permanent magnet]]s, if the magnets are hard (the magnets do not vary in strength with external fields). Earnshaw's theorem forbids [[magnetic levitation]] in many common situations.

If the materials are not hard, [[Werner Braunbeck]]'s extension shows that materials with relative [[magnetic permeability]] greater than one ([[paramagnetism]]) are further destabilising, but materials with a permeability less than one ([[diamagnetism|diamagnetic]] materials) permit stable configurations.