Electric field inside a conductor under influence of non uniform electric field Suppose a conductor is placed in a non uniform external electric field. Why does  the field inside the conductor remain zero?
 A: When you make such claims, you must keep one thing in mind - you are talking about steady state.
So why does the Electric Field inside the conductor become zero in steady state? If it was not zero the free electrons will still keep moving and hence the state will not be so steady. When you say steady state, you mean no movement of particles in this case. This state is achieved after keeping the conductor in the external field for a long time.
When this state is reached, all the charges reside on the surface of the conductor in such a way that the net field inside the conductor is zero. This is following Gauss Law. Hence the movement of free of electrons inside the conductor stops.
It does not matter what kind of external field is present, this will always happen.
Hope this clears your doubt.

P.S. If you have any more doubts,comment below.
A: In the absence of a source of power, any electric field inside a conductor will cause the free electrons to flow until the resultant field in the conductor is zero.  In the absence of a field, the electric potential must be the same at all points in the conductor.
