Drift velocity: When a potential difference is applied across the ends of a conductor, the free electrons in it move with an average velocity opposite to direction of electric field. which is called drift velocity of free electrons.
Drift velocity vd = eEτ / m = eVτ / ml
where, τ = relaxation time, e = charge on electron,
E = electric field intensity, l = length of the conductor
V = potential difference across the ends of the conductor
m = mass of electron.
Mobility: The drift velocity of electron per unit electric field applied is mobility of electron.
Mobility of electron (μ) = vd / E
Its SI unit is m2s-1V-1.
Relation between current and drift velocity:
Consider a conductor XY of length L and area of cross section A (Fig ). An electric field E is applied between its ends. Let n be the number of free electrons per unit volume. The free electrons move towards the left with a constant drift velocity vd.
The number of conduction electrons in the conductor = nAL
The charge of an electron = e
The total charge passing through the conductor q = (nAL) e
The time in which the charges pass through the conductor, t = L/vd The current flowing through the conductor,
The current flowing through a conductor is directly proportional to the drift velocity. From equation (1),
Hence
