Drift Velocity

Step 1: Understanding the relation between drift velocity and length of conductor.
The drift velocity ( ) of electrons is given by the formula: where: - is the current, - is the number of electrons per unit volume, - is the cross-sectional area of the conductor, - is the charge of an electron. In the case of a conductor with a constant potential difference, the current remains the same because . However, the resistance of the conductor ( ) is given by: where is the length of the conductor and is its resistivity. If the length is doubled, the resistance doubles, which means the drift velocity is inversely proportional to the length of the conductor. Step 2: Conclusion.
Thus, if the length of the conductor is doubled, the drift velocity of electrons will be halved.

Step 1: Drift velocity and potential difference.
In electric conduction, the drift velocity of free electrons in a conductor is directly proportional to the applied potential difference . This is a consequence of Ohm's law, which states that current is proportional to the potential difference , and since current is related to drift velocity, the drift velocity follows the same relationship.
Step 2: Explanation of the relationship.
The drift velocity is given by the formula , where is the mobility of the electrons and is the electric field, which is related to the potential difference by , where is the length of the conductor. Hence, is proportional to .
Step 3: Conclusion.
Thus, the correct relationship is that drift velocity is proportional to the potential difference .