Earnshaw's theorem
Statement on equilibrium in electromagnetism / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Earnshaw's theorem?
Summarize this article for a 10 year old
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. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually cited in reference to magnetic fields, but was first applied to electrostatic field.
This article needs additional citations for verification. (February 2021) |
Earnshaw's theorem applies to classical inverse-square law forces (electric and gravitational) and also to the magnetic forces of permanent magnets, 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, 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 (diamagnetic materials) permit stable configurations.