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Prove. The resistivity is given by
ρ = E/J
where E is the electric field intensity and J is the current density.
Proof. Let Va and Vb be the potentials at two points on a conductor separated by a distance L. Then the potential gradient is given by (Va - Vb )/L and the electric field intensity E is equal to the potential gradient so
1) E = Vab/L
Combining 1) and 2) gives
Rearranging 3) yields