I am wondering about the order of operations concerning the Lorentz transformation of fields and the superposition of fields. I was given a problem: Two positively charged electrons start at the origin and then travel along the x axis at a constant speed v in opposite directions. Calculate the electric field in the (far) radiation zone. My approach was to first transform the electric potential field from each electron's rest frame to the lab frame. Then, in the lab frame I added the two fields together via superposition. Afterward, I calculated the electric field making approximations for the (far) radiation zone. Is there something fundamentally wrong with this approach? Why?