Consider a model for a metal in which the lattice of positive ions forms a container for a classical electron gas with n electrons per unit volume. In equilibrium, the average electron velocity is zero, but the application of an electric field produces an acceleration of the electrons. If we use a relaxation time t to account for the electron-lattice collisions, then we have the equation

(a) Solve the equation for the drift velocity in the direction of the applied electric field.
(b) Verify that Ohm’s law is valid, and find the resistivity as a function of n, e, m, and the relaxation time t.

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dv m +=v=-eE dt T