# Drift velocity question

I'm studying about Drude's model. Given that τ is the average time between the electrons' collisions with the ions and the applied electric field is E, we have: $$a=\frac{eE}{m_e}$$ where e is the electron charge and me the electron mass. We know that for an accelerating movement the change in speed is given by : $$Δv=at=>\\Δu=\frac{eE}{m_e}t$$ Now if we substitute t with τ we get what's called drift velocity. $$u_d=\frac{eE}{m_e}τ=μE$$ My textbook says the following :

In a time interval t each electron moves a distance $$u_dt$$

Shouldn't he have used : $$Δx=\frac{1}{2}at^2$$ since the drift velocity is not the average velocity?

• – anna v Nov 24 '17 at 16:54
• The diffusion velocity averages out to zero. The drift (field induced) does not. Please clarify your confusion. – Jon Custer Nov 24 '17 at 16:55
• @Sorry for my rusty English. In an accelerating movement , to find the distance covered we multiply the time by the average speed. However, the author didn't do this here. Ud is given by acceleration times τ, which gives the average speed before every collision and not the average speed while the electron is travelling until the collision. – John Katsantas Nov 24 '17 at 16:57
• @JonCuster I hope it's more clear now, I edited the question. – John Katsantas Nov 24 '17 at 17:06
• Possibly relevant : Drift velocity in Drude model – sammy gerbil Nov 24 '17 at 19:48