When a potential difference is applied across a metal wire, each free…

The correct answer is Option (3) → the electrons keep colliding with the ions of the metal and lose the speed they gain between collisions

Between collisions a free electron is acted on by the force \( -e\vec{E} \) and does accelerate. The collisions with the ions of the metal keep interrupting this, and the average time between them is the relaxation time \( \tau \). On the average, the electrons get only a steady drift velocity \( \vec{v}_d=-e\vec{E}\tau/m \).

Option (1) the electric field inside the wire falls to zero as soon as the current is set up — Incorrect. A steady current needs a field inside the wire all the time. If the field became zero, the electrons would lose their drift and the current would stop.

Option (2) the force on each electron is balanced by the magnetic force due to the current in the wire — Incorrect. A magnetic force \( q\vec{v}\times\vec{B} \) acts at right angles to the velocity of the electron. So it cannot balance the force of the field along the wire.

Option (3) the electrons keep colliding with the ions of the metal and lose the speed they gain between collisions — Correct. The repeated cycle of acceleration and collision keeps the average drift speed steady.

Option (4) the mass of an electron is so small that the force produces no acceleration — Incorrect. A small mass makes the acceleration \( eE/m \) large. The electrons do accelerate between collisions.

NCERT (2026-27):
Example 3.2 – “(b) Each ‘free’ electron does accelerate, increasing its drift speed until it collides with a positive ion of the metal. It loses its drift speed after collision but starts to accelerate and increases its drift speed again only to suffer a collision again and so on. On the average, therefore, electrons acquire only a drift speed.”