A current-carrying wire has a cross-sectional area that gets smaller towards the end of the wire. The current has the same value for each section of the wire such that the charge does not accumulate at any one point. What is the change in the drift velocity as the area becomes smaller?

The correct answer is option 2) i.e. vd ∝ E

CONCEPT:

• Drift velocity: The average velocity attained by the electrons under the influence of an electric field is termed the drift velocity. 
  • The free electrons are always in a constant random motion in the conductor.
  • When the conductor is connected to a battery, an electric field is generated.
  • When these free electrons are subjected to an electric field, they slowly drift in the direction of the electric field applied, while maintaining the random motion.
  • At this point, the net velocity of the electrons is called its drift velocity.

The drift velocity (vd) of the electron in a conductor is given by:

\(v_d =\frac{I}{nAq}\)

Where I is the current flowing through the conductor, A is the area of cross-section of the conductor, q is the charge on the electron and n is the number of electrons.

EXPLANATION:

• Since the current remains the same along the length of the conductor, \(v_d \propto \frac{1}{A}\)
• Therefore, as the cross-sectional area becomes smaller, the drift velocity increases.