I am referring to Ashcroft/Mermin - Solid state physics. After stating the assumptions of the Drude model,they go on to derive the Ohm's law starting with j = -neV.
Where j is the current density, n is the number of electrons per unit volume, e is the charge of an electron and V, the average velocity of an electron. Now, keeping the assumptions of the drude model in mind,the aevrage velocity of the electrons in the absence of an electric field (or any other force) should be zero. In presence of an electric field E, the avg velocity would be due to the electric field (let us assume it is constant in this case) : Vavg = -(eET)/m where T is the average relaxation time of the electrons.
Now this is where confusion arises: how could using the average relaxation time yield average velocity of an electron? the avg T would give us the average time an electron spends between 2 collisions, and hence the velocity obtained using it would give us the average of the "final velocities" obtained by the electrons, i.e., the average of the velocities electrons would have just before a collision.
Intuitively, and also mathematically shouldn't the actual average velocity of the electrons be half the one obtained above ( the avg velocity of a particle with constant acceleration would be midway its initial and final velocities) ?.
