Cavity inside a conductor

Cavity inside the conductors and conducting shells

According to the definition of conductivity (sigma=J//E) , electric field is being considered to exist inside a conductor but according to electrostatics of conductor , electric field cannot exist inside its volume. Explain the difference and state the condradiction if any.

The electric field inside a conductor

Electric field inside a conductor can be zero only, if potential inside the onductor is

Assertion (A): In a cavity in a conductor, the electric field is zero. Reason (R ): Charges in a conductor reside only at its surface.

If n,e,A and v_(d) are free electron density inside conductor , charge of electron , area of cross-section of conductor and drift velocity of free electrons inside conductor, then current l through the conductor is