Why don't we take drift velocity as the average velocity of electrons?

[tan99]

Drift velocity, v_d = eEτ/m_e

Drift velocity, as in the current formula I=nev_dA should correspond to the average velocity with which the electrons are moving in the steady current, but the formula at top gives the mean FINAL velocity achieved by the electrons in short spurts of time(mean relaxation time, τ).
Since distance d=0.5aτ² , the average velocity

v=d/τ=0.5eEτ/m_e

Shouldn't this be a better formula??

PS: The average initial velocity u is 0 I believe...

 

[eljose79]

Hello there,

Thank you for bringing up this interesting topic about drift velocity. I would like to clarify a few things regarding this formula.

Firstly, the formula vd = eEτ/me is correct and is used to calculate the drift velocity of electrons in a steady current. This formula takes into account the mean relaxation time, τ, which is the average time between collisions of the electrons with the lattice of the material. Therefore, it gives us the mean final velocity achieved by the electrons after multiple collisions.

The formula you suggested, v=d/τ=0.5eEτ/me, is not an accurate representation of the average velocity of electrons in a steady current. This formula only takes into account the distance traveled by the electrons in a certain time period, but it does not consider the effect of collisions on the velocity of electrons.

Moreover, the average initial velocity, u, is not necessarily 0 in this scenario. It depends on the material and the conditions under which the current is flowing. In some cases, the electrons may already have some initial velocity before entering the material, and in other cases, they may be accelerated by an external electric field.

In conclusion, the formula vd = eEτ/me is the correct representation of the drift velocity of electrons in a steady current and it takes into account the mean relaxation time, τ, which is a crucial factor in determining the final velocity of electrons. I hope this clarifies any confusion and thank you for your contribution to this discussion.