What is the microscopic form of ohm’s law?

The microscopic form of Ohm’s law is J =σ E, where σ is the electrical conductivity, E the electric field and J the current density .

This form of Ohm’s law operates on a microscopic level relating the current density J to the conductivity σ and the electric field E.

We know that the current I = A nev_{d}

where A is the area of cross-section ,n the number density of electrons, e the charge on each electron and vd the drift velocity of electrons.

Current density J at a point in a conductor is the amount of current flowing per unit area of the conductor around that point provided the area is held in a direction normal to the current.