Up to which precision has the coulomb law proven to be true? I.e. if you have two electrons in a vacuum chamber, 5 meters appart, have the third order terms been ruled out? Are there any theoretical limits to measure the precision ( Planck's constant?). Obviously there are practical limitations ( imperfect vacuum, cosmic rays, vacuum fluctuation). Still, does anyone know what was the smallest amount ever correctly predicted by that law?
Edit : Summary
On the high end of the energy spectrum a precision of 10^-16 has been shown ( 42 years ago )
For electron point charges at large distances the law might brake down due to practical reasons.
For moving particles QED gives a correction to the law: http://arxiv.org/abs/1111.2303