According to Special Relativity, the usual Coulomb force law is only valid for stationary charges. In case of moving charges, there is an additional factor (see for instance Sect.5.3.4 in http://www.damtp.cam.ac.uk/user/tong/em/el4.pdf ) f=(1-v^2/c^2) / ( 1-v^2*sin^2(θ)/c^2 )^1.5 where v is the velocity of the charge relative to the stationary test charge, θ the angle between v and the radius vector between the two and c the speed of light. For v/c<<1, we can use a Taylor expansion of the denominator to yield f ≈ (1-v^2/c^2) * (1+1.5*v^2*sin^2(θ)/c^2) ≈ ≈ (1- v^2/c^2*(1-1.5*sin^2(θ)) ) If we have a random distribution for the direction of v, we have to average over sin^2(θ), which yields a constant factor 1/2. So the relativistic factor for an isotropic distribution of the velocity vector is f_av ≈ (1- v^2/c^2*(1-0.75) ) = 1 - v^2/4c^2 Now for practically all states of matter, the electron speed is several orders of magnitudes higher than that of the ions. The electrons making up atoms and ions for instance have speeds of about 10^6 m/sec , which would imply 1-f_av,el ≈ 3*10^-6 In contrast, 1-f_av for the ions would be several orders of magnitude smaller, so any mass that is neutral at rest, would become charged by a fraction 1-f_av,el. So for instance for a 100 ml glass of water, this would amount to about 16 Coulombs, and two glasses of water at 1 m distance would repel each other with the incredible force of 2*10^12 Newton. And that would be even negligible compared to the forces with which other objects would repel the water and each other. Basically, the whole universe would fly apart. Any resolutions for this apparent paradox?