We assume that there is no electric field inside the perfect conductor because relaxation time of metal is very short. whereas J=sigma*E But if this is the case, how can current flow inside the metal? -Is this because of battery? If there is a battery connected to a metal wire, it will create a potential difference between both ends. And such potential difference is maintained by the battery and that is why there is a current despite of the short relaxation time? -if that's the case then, applying a strong enough external electric fields can create currents in the conductor, which means there is a certain amount of electric fields inside the conductor? -Can I understand the concept this way. "If charge density is constantly created at a faster rate than relaxation time, there is a current inside the metal."