# Drift velocity formula derivation confusion

1. May 14, 2013

### swap1996

In the derivation of drift velocity i have seen two variations and want to know which one's correct.
• s=ut +$\frac{1}{2}$a$t^{2}$
Assume that the drift velocity of any electron in any conductor is :
$v_{d}$=l/t
Due to the electric field the acceleration of electrons in any conductor is:
a=eE/m
Now the distance travelled by an electron after a long time (initial thermal velocity = 0)
l=$\frac{at^{2}}{2}$
the time between the collisions is τ ∴
l=$\frac{eEτ^{2}}{2m}$
thus the velocity is
$v_{d}$=$\frac{eEτ}{2m}$

• In another proof i saw the author using v=u+at⟹$v_{d}$=$\frac{eEτ}{m}$
My question is which of the the two equations of motion can be used in the proof? Can they be used at all.

Last edited: May 14, 2013
2. May 20, 2013

### projjal

Since we are talking about 'average velocity' so the former derivation would be appropriate.However i don't think using classical mechanics for finding the velocity of particles like electrons would be appropriate,i think this requires quantum mechanical approach.

3. May 20, 2013

### ZapperZ

Staff Emeritus
It is appropriate when the limits of the validity of such an approach is taken into account. The Drude model is based on such an approach (which is where we get the beloved Ohm's Law). So it is valid whenever appropriate.

Zz.