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