Relation between electric conductivity(σ) and current density (J)

# “Relation between electric conductivity(σ) and current density (J)”:

Considered the length of current carrying conductor be (l) and its area of cross section be A. when V volt potential difference is applied by the cell across the conductor, the electric field E is produced and current I ampere is flowing through it.

we know that :
Electrical conductivity=1/Electric resistivity

σ = 1/ρ --------(1)

Current density = current/Area
J = I/A -------(2)

By the definition:
Resistivity, ρ = (R×A)/l

(By ohm's law, V = R×I
Hence, R = V/I )

ρ = V/I × A/l

ρ = V/l × A/I

( Since, Electric field, E = ∆V/∆X = V/l )

ρ = E × A/I

Putting the value of ρ in enq1

σ = 1/E × I/A

( Putting, I/A = J )

σ = 1/E × J

σ.E = J

Or [ J = σ.E ]