[Electromagnetism] perfect conductor and Current

[kidsasd987]

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."

 

[kidsasd987]

I looked for some articles and found that there is no electric field inside the conductor 'only' at static equilibrium.

Does this mean that if strong enough electric fields are applied at t=0, it will go through a transient state and reach to the state that current density(electric field) exists in the condudctor?

 

[vanhees71]

The electric field is 0 in conductors only in the static case, i.e., for time-independent fields and charge distributions and $\vec{j}=0$. In the stationary case, where you have time-indpendent fields and charge and current densities, there is an electric field within the conductor and in linear-response approximation it's given by Ohm's Law, $\vec{j}=\sigma \vec{E}$.