Question

The drift velocity of electrons (v) in a current-carrying conductor is related to its electric field (E) as:
1. vd ∝ E²
2. v_d ∝ E
3. vd ∝ √E
4. vd ∝ E^-1

Answer 1

Correct Answer - Option 2 : v_d ∝ E

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 (v_d) 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.

• Mobility is defined as the magnitude of drift velocity per unit electric field. 

Mobility, \(μ = \frac{v_d}{E}\)

EXPLANATION:

Mobility, \(μ = \frac{v_d}{E}\) ⇒ v_d = μE 

⇒ vd ∝ E