Consider a train moving at speed 's' and there is a charge particle at rest relative to the observer at train. The second observer on a ground see the charge particle and observer moving relative to him, and infer the existence of a magnetic feild strong enough that its feild is significant at few centimeters from the charged particle. He decides to shoot an arrow with a circular loop hinged on it and there is a LED attach to the loop. The observer at ground shoot the arrow as he see the train coming near him. The arrow passes near to the charge particle (say a few centimeteres away that he could feel the magnetic influence predicted by observer on ground). according to the observer on ground the change in magnetic flux from the loop will induce an emf and current will flow, this will light up the LED, whereas from the point of view of observer on train there is no magnetic feild so the LED should not glow relativity says that the observer in each frame will conclude the same no matter their perception is different to explain the phenomena, but in scenario described above they both come at a different conclusion, where i got wrong(if i did)?