Question

Is there any electric field inside a perfect conductor? Is there any conduction current inside a perfect conductor? Can static magnetic fields exist in a perfect conductor?

Answer 1

A perfect conductor is one, which has infinite conductivity or zero resistivity.

Now, since electric fields create forces on electric charges, there cannot be static electric fields present inside perfect conductors. If a field was present inside a perfect conductor, the charges inside the conductor would feel an electric force and hence move in response to that force. Thus, there would have exist a resistance, which in turn, is not possible for a perfect conductor.

The current density is defined by the history of E(t), i.e. the time varying electric field. Zero (DC) resistance does not mean infinite acceleration.Conductivity is defined as the linear response in a steady state that is achieved when the perturbation is turned on adiabatically from t=−∞. So zero resistance (or infinite conductivity), tells us the current will be infinite after the non-zero electric field has been applied for eternity!

Thus, a current exists and flows with infinitely high value after a certain time, since the conductivity is infinite.

From Faraday's law of electromagnetism, we know that, curl E = - (del B / del t). Hence, if there is some time varying magnetic field inside a perfect conductor, then E would not be zero. Hence, there can exist a static magnetic field, which may or may not be zero, inside a perfect conductor.