On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time.
Answers
Consider in the wire that there are n free electrons per unit volume moving with the drift velocity vd
In the time interval Δt each electron advances by a distance vdΔt and volume of this portion is AvdΔt and no of free electron in this portion is nAvdΔt and all these electrons crosses the area A in time Δt
Hence charge crossing the area in time Δt is
ΔQ=neAvdΔt
or
I=ΔQ/Δt =neAvd
This is the relation between the electric current and drift velocity
If the moving charge carriers are positive rather than negative then electric field force on charge carriers would be in a direction of electric fields direction and drift velocity would be in left to right direction opposite to what shown in fig-1
In terms of drift velocity current density is given as
j=I/A=nevd