I have been trying to understand why the net electric field inside a conductor is zero regardless of the exterbal electric field. But why should equilibrium ever be attained?
See the diagrams below.
The top diagram shows a conductor with no external field applied. Note that the charges are randomly distributed within the conductor. Since there is no external field there is no field within the conductor as well.
The bottom diagram shows the same conductor in the presence of an constant external field perpendicular to the length of the condutor. By convention, the direction of the electric field is the direction of the force that a positive charge would experience if placed in the field. So the free electrons inside the conductor experience a force moving them to the left side of the conductor leaving the right side of the conductor positively charged. The charges have rearranged themselves until they no longer experience a force. Bottom line, equilibrium is established within the conductor.
Now note the direction of the electric field within the conductor. It is equal and opposite to the direction of the field external to the conductor. Keep in mind that the external field passes through the conductor. So there a net field within the conductor of zero.
If the external field were parallel to the conductor and the conductor was part of a closed circuit, current would flow in the conductor.
Hope this helps.