drive relation between current density conductivity and electric field
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!
