# Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.

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When a conductor is placed in an electric field, it will experience a force ,F = qEsince a conductor has free electones ,F = -eE(-e = charge of an electrone = -1.6 * 10^-19)

But F = ma (Newton's law )

therefore , ma = -eE

=a = (-eE ) / m

But thay are not able to move in a straight line due to collision with other particles but can drift in a particular direction due to electric field .

Thus each elecrone will acquire different velocities v1 , v2 , v3 ....

Total average velocity , Vd= (v1 + v2 + v3 ... + vn) / N

v = u+at

Vd= ( u1 + u2 + u3 + ... + un) / N + ( a * T1 + a* T2 + ... a * Tn) / N

( T1 +T2 +...+ Tn are the relaxation time of each electrone )

= a * T ( T - relaxation time )

Therefore Vd= a * T

Vd= -eET / m