Question

Define drift velocity of free electrons and write the relation between drift velocity and current density.

Hint:

Drift velocity is the average speed of electrons moving in response to an electric field, and it is related to the current density through the equation \( J = n e v_d \).

Answer 1

Step 1: Definition of drift velocity.
Drift velocity is the average velocity of free electrons in a conductor due to an applied electric field. It is the net velocity that the electrons acquire under the influence of the electric field, superimposed on their random thermal motion.
Step 2: Relation between drift velocity and current density.
The relation between drift velocity \( v_d \) and current density \( J \) is given by Ohm's law in terms of electron drift: \[ J = n e v_d \] where: - \( J \) is the current density (in A/m²), - \( n \) is the number of free electrons per unit volume, - \( e \) is the charge of an electron (approximately \( 1.6 \times 10^{-19} \, \text{C} \)), - \( v_d \) is the drift velocity (in m/s).
Step 3: Conclusion.
The drift velocity \( v_d \) is directly related to the current density \( J \) by the equation \( J = n e v_d \).