Website owner:  James Miller

Prove. The resistivity is given by

ρ = E/J

where E is the electric field intensity and J is the current density. 

Proof. Let V_a and V_b be the potentials at two points on a conductor separated by a distance L. Then the potential gradient is given by (V_a - V_b )/L and the electric field intensity E is equal to the potential gradient so

1)        E = V_ab/L

Now

Combining 1) and 2) gives

Rearranging 3) yields