Here's how the drift velocity of electrons in a metallic conductor changes when you double the length while keeping the applied potential difference constant:

Understanding Drift Velocity

* Drift velocity (v_d) is the average velocity at which free electrons move through a conductor under the influence of an electric field. It's a very slow speed compared to the random thermal motion of electrons.

* Current (I) is directly proportional to the drift velocity. A higher drift velocity means more charge carriers pass a point per second, resulting in a larger current.

The Relationship

The key equation relating drift velocity, electric field (E), and electron mobility (µ) is:

v_d = µE

Let's break down how this equation changes when you double the length:

1. Electric Field: The electric field (E) is the potential difference (V) divided by the length (L) of the conductor:

E = V/L

2. Double the Length: When you double the length, the electric field is halved (since V is constant). This means:

E' = V / (2L) = E/2

3. Drift Velocity: Since drift velocity is directly proportional to the electric field, doubling the length will also halve the drift velocity:

v_d' = µ(E/2) = (1/2) v_d

Conclusion

When you double the length of a conductor while keeping the applied potential difference constant, the drift velocity of the electrons is halved. This is because the electric field within the conductor is reduced, leading to a slower average movement of the electrons.