Question

Define Drift Velocity and establish its relation with electric current.

Hint:

Important formulas: - Drift velocity: \( v_d = \mu E \) - Current relation: \( I = nqAv_d \) - Even though drift velocity is small, current appears instantly due to electric field propagation.

Answer 1

Drift Velocity
Drift velocity is defined as the average velocity acquired by free charge carriers (such as electrons) in a conductor when an electric field is applied across it. Under the influence of an electric field, the electrons move in a particular direction opposite to the direction of the field. This slow and steady motion of electrons is called drift velocity.

Relation between Drift Velocity and Electric Current
Consider a conductor of cross-sectional area \(A\) containing free electrons. Let the number of free charge carriers per unit volume be \(n\). When an electric field is applied, each charge carrier moves with an average drift velocity \(v_d\).

In time \(t\), the electrons move a distance
\[ \text{distance} = v_d t \] The volume of the conductor through which electrons move in time \(t\) is
\[ \text{Volume} = A \times v_d t \] The number of charge carriers in this volume is
\[ \text{Number of electrons} = n A v_d t \] If the charge on each electron is \(e\), the total charge flowing through the cross-section in time \(t\) is
\[ Q = n A v_d t \times e \] Electric current is defined as the rate of flow of charge:
\[ I = \frac{Q}{t} \] Substituting the value of \(Q\):
\[ I = \frac{n A v_d t e}{t} \] \[ I = n e A v_d \] Result
The relation between electric current and drift velocity is
\[ I = n e A v_d \] where
\(n\) = number of charge carriers per unit volume
\(e\) = charge of an electron
\(A\) = cross-sectional area of the conductor
\(v_d\) = drift velocity of electrons

Conclusion
Thus, electric current in a conductor is directly proportional to the number of charge carriers, their charge, the cross-sectional area of the conductor, and the drift velocity of the charge carriers.