A charge sitting near a metallic plate will induce a mirror charge of the same amount on the plate. Will the induced mirror charge q' be the same if they would be moving with respect to each other, i.e. q'=q? or will it be like q'=γq ? I am asking this, for the following case, a charge in a metallic pipe, because in the lab (pipe) frame, the radial component of the electric field gets stronger with γ, so I expected the induced charge will be higher, by the same amount γ. I am confused, please help.