Due to Earnshaw's theorem, no static arrangement of classical electrostatic fields can be used to stably levitate a point charge. There is an equilibrium point where the two fields cancel, but it is an unstable equilibrium. By using feedback techniques it is possible to adjust the charges to achieve a quasi static levitation.
Earnshaw's theorem holds that a charged particle suspended in an electrostatic field is unstable, because the forces of attraction and repulsion vary at an equal rate that is proportional to the inverse square law and remain in balance wherever a particle moves. Since the forces remain in balance, there is no inequality to provide a restoring force; and the particle remains unstable and can freely move without restriction.
Levitation
The first electrostatic levitator was invented by Dr. Won-Kyu Rhim at NASA's Jet Propulsion Laboratory in 1993.[4] A charged sample of 2 mm in diameter can be levitated in a vacuum chamber between two electrodes positioned vertically with an electrostatic field in between. The field is controlled through a feedback system to keep the levitated sample at a predetermined position. Several copies of this system have been made in JAXA and NASA, and the original system has been transferred to California Institute of Technology with an upgraded setup of tetrahedra four beam laser heating system.
On the Moon the photoelectric effect and electrons in the solar wind charge fine layers of Moon dust on the surface forming an atmosphere of dust that floats in "fountains" over the surface of the Moon.[5][6]
^Samuel Earnshaw "On the Nature of the Molecular Forces which regulate the Constitution of the Luminiferous Ether," Transactions of the Cambridge Philosophical Society, Cambridge University Press, Vol. 7, pp. 97–122 (1842).
^James Clerk Maxwell, A Treatise on Electricity and Magnetism, Macmillan and Co., "Earnshaw's theorem" p. 139 (1873)
