Direction of electric field and electron force

In a conductor, if an electric field $\vec E$ is applied, the force on an electron is $\vec F = -e\vec E$ since the electron has charge $-e$.

Therefore, electrons move opposite to the direction of the electric field.

Relation with potential

The electric field points from higher potential to lower potential. Since electrons move opposite to $\vec E$, they drift from lower potential to higher potential.

Nature of motion inside a metal

Free electrons in a metal do not move in straight lines with uniform velocity because they continuously collide with lattice ions.

Their actual motion is:

• random and zig-zag due to thermal motion,
• with a small average drift velocity opposite to the field.

Hence their paths are effectively curved/irregular, not straight.

Checking options

• A: "move in the straight line paths in the same direction"
  False. Electrons suffer frequent collisions, so paths are not straight.

• B: "move with the uniform velocity throughout from lower potential to higher potential"
  False. Though drift is from lower to higher potential, velocity is not uniform throughout because of collisions.

• C: "drift from higher potential to lower potential"
  False. Electrons drift from lower to higher potential.

• D: "move in the curved paths from lower potential to higher potential"
  True.

Final answer

The correct option is $\boxed{D}$