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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 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

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