Understanding the behavior of free electrons in a conductor is crucial when they drift from a region of lower potential to a region of higher potential. Let's clarify this:
Within a conductor, free electrons are in constant, random motion due to thermal energy. The application of an electric field (resulting from a potential difference across the conductor) exerts a force on these electrons, causing them to "drift." This drift occurs in the direction opposite to the applied electric field. As electrons possess a negative charge, they move from areas of lower potential towards areas of higher potential, driven by the electric field's force.
Although the majority of free electrons do exhibit a drift from lower to higher potential (contrary to the electric field's direction), it is important to recognize that individual free electrons do not all move uniformly at any given instant.
No, free electrons within a conductor do not all move in the same direction when drifting under an applied electric field. While there is an overall drift from lower to higher potential, their random thermal motion results in diverse directional movement. The drift phenomenon represents a minor, net displacement superimposed upon their random movements.