Question

Distinguish between drift velocity and mobility. Establish a relation between drift velocity and current.

Answer 1

Drift velocity is defined as average velocity with which free electrons get drifted towards the positive end of a conductor under the influence of the external electric field.

Mobility μ is defined as the magnitude of drift velocity per unit electric field.
If vd is the magnitude of the drift velocity when electric filed applied is E, then 
μ=vd/E-----------(1)

The S.I unit of mobility is m2/VS

Relation between Current and drift velocity :

Consider a metallic conductor of length l and uniform are of cross section A.

Let n be the number of free electrons per unit volume in metal.

When a potential difference V is applied across the ends of the condutor,
the electric filed E= V/l
Because of the electric field the free electrons drift opposite to the eletei field with drift velocity vd.
let the distnce moved by free electrons be equal to vd Δt [ short interval of time].

Volume of conductor= AvdΔt

The number of electrons drifting in this volume is nAvdΔt

as charge on electron is -e, the total charge transported across area A is -enAvdΔt

The amount of charge transported in a time Δt across the area of cross section A in direction opposite to electric field  is ΔQ=enAvdΔt

If I is the magnitude of current in conductor, ΔQ=I Δt

∴ I Δt=n e A vd Δt------------(1)
I=n e A vd
gives the relation between current and drift velocity.