When I studied special relativity for the first time, I encountered the exemple of a infinite neutral wire in the laboratory frame of reference, R, through which a constant current is running. In this frame of reference, the electrons in the wire are moving with a velocity +v and the ions are stationary, the electric field is zero and there is a non zero magnetic field. Now, from the point of view of a frame of reference R' which is moving with a velocity +v relative to R, the electrons are stationary and the ions are moving with velocity -v, but the wire is not neutral because of Lorentz contraction : the ions are denser than in R and the electrons are less dense than in R. The wire is positively charged in R' and then the electric field is not equal to zero. This example illustrates how the magnetic field seen in R is a relativistic effect of the motions of charges. If this is coorect, I still have questions : 1. The universe is neutral in R. If it had to be also neutral in R' and the wire is positively charged, where the negative charges needed to make the balance are located? 2. Even though the electrons are moving in R, their density is considered equal to that of the ions which are not moving, in other words the Lorentz contraction has not been taken into account in R, why? Is there something special with this frame of reference? Is this related to the center of mass frame of reference?