The validity of Ohm's law is examined for the case of electric fields which are changing either in amplitude or direction over distances comparable to one electron mean free path within a metal. By perturbing both the amplitude and spatial variation of the electric field, an approximate solution of Boltzmann's equation is obtained which yields a first-order correction to Ohm's law that is, in general, not in the same direction as the linear J = σE term. The nonlinear term is quadratic in the electric field amplitude and depends on the spatial derivatives of the electric field.

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