Derive the Drift Velocity Equation

(The drift velocity is the average velocity of a charge carrier due to an electric field)Consider a conductor with length l and cross sectional area AThere are n electrons per unit volume (m³) moving through the conductor with drift velocity vThe distance travelled by an electron travelling at speed v in time dt is: l = vdtThe volume of the conductor is: V = AlTherefore V = A*(vdt)Since n is the number of electrons per m³ , the total number of electrons in that section of the conductor is = nA*(vdt)so the total charge Q = nAvdte (where e is charge on 1 electron)Since current is defined as I = Q/dtI = (nAvdte)/dt and the "dt" cancels out leaving you with the equation for drift velocity in a conductor:I = nAve