# When a potential difference is applied across the ends of a conductor, how is the drift velocity of the electrons related to the relaxation time ?

The relation of drift velocity with electric field is given by

$v_d=\frac{Ee}{m}\tau$

$E=\frac{V}{l}$

Therefore

$v_d=\frac{Ve}{lm}\tau$

Where

vd is drift velocity, V is the potential difference applied across the ends of the conductor

l is the length of the conductor, $\tau$ is the relaxation time and e and m are charge and mass of the electron respectively.

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