Hello,

Current density is represented by J

Conductivity is represented by (sigma) σ

Electric field is represented by E

We will derive the relation between the three quantity by Ohms Law and by relation of Resistance with resistivity.

OHM'S Law : .        V = I R

R = (rho × L) / A  Substitute this value in Ohms law

V = ( I × rho × L ) / A

( V / L ) / rho = I / A

E σ  = J [  V/ L  = E ] [ I / A = J ] [ 1 / rho= σ ]

For any metallic conductor in consideration, if the specific resistance is ρ, then conductivity, σ=1/ρ and now, according to the definition of specific resistance:

ρ=EJ where, E is the intensity of electric field at a point inside the conductor and J is the current density.

∴σ=JE

or J =σE .

So, the relation between J and E is that J =σ E

Hope I have answered your question. All the best!