Editing Earnshaw's theorem (section)

=== Loopholes ===
Earnshaw's theorem has no exceptions for non-moving permanent [[ferromagnetism|ferromagnets]].  However, Earnshaw's theorem does not necessarily apply to moving ferromagnets,<ref name=":0">{{cite journal |last1=Simon |first1=Martin D. |last2=Heflinger |first2=Lee O. |last3=Ridgway |first3=S.L. |date=1996 |title=Spin stabilized magnetic levitation |journal=American Journal of Physics |volume=65 |issue=4 |pages=286–292 |doi=10.1119/1.18488}}</ref> certain electromagnetic systems, pseudo-levitation and diamagnetic materials. These can thus seem to be exceptions, though in fact they exploit the constraints of the theorem.

[[Spin-stabilized magnetic levitation]]: Spinning ferromagnets (such as the [[Levitron]]) can, while spinning, magnetically levitate using only permanent ferromagnets, the system adding gyroscopic forces.<ref name=":0" /> (The spinning ferromagnet is not a "non-moving ferromagnet"). 

Switching the polarity of an electromagnet or system of electromagnets can levitate a system by continuous expenditure of energy. [[Maglev (transport)|Maglev trains]] are one application.

[[Pseudo-levitation]] constrains the movement of the magnets usually using some form of a tether or wall.  This works because the theorem shows only that there is some direction in which there will be an instability.  Limiting movement in that direction allows levitation with fewer than the full 3 dimensions available for movement (note that the theorem is proven for 3 dimensions, not 1D or 2D).

[[Diamagnetism|Diamagnetic]] materials are excepted because they exhibit only repulsion against the magnetic field, whereas the theorem requires materials that have both repulsion and attraction.  An example of this is the famous [[Magnetic levitation#Direct diamagnetic levitation|levitating frog]] (see [[Diamagnetism]]).