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. Drift velocity is very small it is of the order of `10^(-4) m//s` as compared to thermal speed `( approx 10^5 m//s)` of electrons at room temperature. (Fig. 1)

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, `rho =` specific resistance, `sigma =` conductivity `(sigma=1/rho)`

then current relates with drift velocity as `i = n eAv_d` we can also write

`v_d=i/(n eA)=J/(n e)=(sigmaE)/(n e)=E/(sigman e)=V/(rhol n e)`

`(1)` The direction of drift velocity for electron in a metal is opposite to that of applied electric field (i.e. current density `vecJ`).
`v_d prop E` i.e. greater the electric field, larger will be the drift velocity

`(2)` When a steady current flows through a conductor of non-uniform cross-section drift velocity varies inversely with area of cross-section `(v_dprop1/A)`. (Fig. 2)

`(3)` If diameter (d) of a conductor is doubled, then drift velocity of electrons inside it will not change. (Fig. 3)

`(4)` `text(Relaxation time)` `(t):` The time interval between two successive collisions of electrons with the positive ions in the metallic lattice is defined as relaxation time `tau=text(mean free path)/text(r.m.s. velocity of electrons)=lamda/v_(rms)`. With rise in temperature `v_(rms)` increases consequently `tau` decreases.

`(5)` `text(Mobility :)` Drift velocity per unit electric field is called mobility of electron i.e. `mu=(v_d)/E`. It's unit is `m^2/(vol t-sec)`