Question

Relation between drift velocity and relaxation time derivation 12 class physics

Answer 1

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Answer 2

Drift velocity is the small average velocity of free electron along the direction of positive potential and is denoted by $v_{d}$

In conductor average time between two consecutive collisions of electrons with ions at the lattice sites is called relaxation time and is denoted by ​τ.

We know F = m.a

and also F = q.E = -e.E

m.a = -e.E

a = $\frac{-e.E}{m}$   .....(i)

We also know $v_{d}$ is average velocity and hence is equal to

Note:- It is assumed that electron after collision forgets it’s past motion and starts a fresh with zero velocity

$v_{d}$ = a. τ            .....(ii)

Combining (i) and (ii)

we get $v_{d}$ = $\frac{-e}{m}$.E.τ