let the N number of electrons crossing length L in T seconds
Number of electrons per unit time is
(N/T)
the total charge passing per unit time is nothing but current
L=Nq/T
as we know that L=vT
I=((Nqv)/L)
Current density is denoted by change J
current passing a unit cross section
J=(L/A)=((Nqv)/(LA))
n is number of electrons per unit volume
n=(N/(LA))
J=nqv
ρ is the charge density and denoted by
nq=ρ
so J=ρv
but we know that v=uE
J=uρE
ρu=σE
σ=nqv
J=σE

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