When do electrons move for the flow of charges in a conducting metallic wire?

Only if there is a difference of electric pressure

The correct answer is option 3. Only if there is a difference of electric pressure.

In a conducting metallic wire, electrons are the charge carriers responsible for the flow of electric current. These electrons move within the wire when there is a potential difference, or voltage, applied across the wire.

When a potential difference exists between two points in the wire, electrons experience an electric force due to the electric field created by this voltage difference. This force causes the electrons to drift in the direction opposite to the electric field. In other words, electrons move from the point of lower electric potential (negative terminal) to the point of higher electric potential (positive terminal).

So, the flow of electrons, and thus the flow of electric charge, occurs only when there is a difference in electric pressure or potential. This is why electrons move for the flow of charges in a conducting metallic wire only if there is a difference in electric pressure.