# Drift Velocity

Drift velocity is the average uniform velocity acquired by free electrons inside a metal by the application of an electric field which is responsible for current through it (Fig. 5). Drift velocity is very small as it is of the order of 10–4 m/s as compared to thermal speed (105m/s) of electrons at room temperature.

Fig. 5

If suppose for a conductor,
n = number of electron per unit volume of the conductor,
A = area of cross section,
V = potential difference across the conductor,
E = electric field inside the conductor,
i = current, J = current density, ρ = specific resistance,
σ = conductivity (σ = 1/ρ), then current relates with drift velocity as i = neAvd. We can also write

• The direction of drift velocity for electron in a metal is opposite to that of applied electric field (i.e., current density ).

Also, vd E, i.e., greater the electric field, larger will be the drift velocity.
• When a steady current flows through a conductor of non-uniform cross section, drift velocity varies inversely with area of cross-section vd 1/A (Fig. 6).
Fig. 6
• If diameter (d) of a conductor is doubled, then drift velocity of electrons inside it will not change.

# Relaxation time (τ)

The time interval between two successive collisions of electrons with the positive ions in the metallic lattice is defined as relaxation time

With rise in temperature, vrms increases, consequently τ decreases.

# Mobility

Drift velocity per unit electric field is called mobility of electron, i.e., μ = vd / E. Its unit is m2/V-s.

Some Important Points
• 1 A of current means the flow of 6.25 ×1018 electrons per second through any cross section of the conductors.
• dc flows uniformly throughout the cross-section of conductor while ac mainly flows through the outer surface area of the conductor. This is known as skin effect.
• It is worth noting that electric field inside a charged conductor is zero, but it is non-zero inside a current, carrying conductor and is given by
• E = V/l, where V = potential difference across the conductor and l = length of the conductor. Electric field outside the current carrying is zero.
Fig. 7
• For a given conductor, JA = i = constant, so that J ∝ 1/A, i.e., J1A1 =J2A2; this is called equation of continuity.
Fig. 8
• If the cross section is constant, I ∝ J, i.e., for a given cross-sectional area, greater the current density, larger will be current.
• The drift velocity of electrons is small because of the frequent collisions suffered by electrons.
• The small value of drift velocity produces a large amount of electric current due to the presence of extremely large number of free electrons in a conductor. The propagation of current is almost at the speed of light and involves electromagnetic process. It is due to this reason that the electric bulb glows immediately when switch is on.
• In the absence of electric field, the paths of electrons between successive collisions are straight line while in presence of electric field the paths are generally curved.
• Free electron density in a metal is given by

where NA = Avogadro number, x = number of free electrons per atom, d = density of metal, and A = atomic weight of metal.