Question

Explain the term drift velocity of electrons in a conductor. Obtain the expression for the current through a conductor in terms of drift velocity.

Answer 1

Drift velocity is defined as the average velocity with which free electrons in a conductor get drifted in a direction opposite to the direction of the applied electric field. Let n be the number of free electrons per unit volume of the conductor. Then, total number of free electrons in the conductor = $n\times$ volume of the conductor $=n\times Al$.

If e is the magnitude of charge on each electron, then the total charge in the conductor, Q = (nA/)e ...(i)
The time taken by the charge to cross the conductor length is given by
$t=\frac{l}{V_d},$ where vd is drift velocity of electrons.
According to the definition of electric current,
$l=\frac{Q}{t}=\frac{nAlc}{\frac{l}{v_d}}=neA{v}_d$
$l=neA{v}_d$