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## Main Question or Discussion Point

In the derivation of drift velocity i have seen two variations and want to know which one's correct.

- s=ut +[itex]\frac{1}{2}[/itex]a[itex]t^{2}[/itex]

Assume that the drift velocity of any electron in any conductor is :

[itex]v_{d}[/itex]=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=[itex]\frac{at^{2}}{2}[/itex]

the time between the collisions is τ ∴

l=[itex]\frac{eEτ^{2}}{2m}[/itex]

thus the velocity is

[itex]v_{d}[/itex]=[itex]\frac{eEτ}{2m}[/itex]

- In another proof i saw the author using v=u+at⟹[itex]v_{d}[/itex]=[itex]\frac{eEτ}{m}[/itex]

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