Question

Find the relation between drift velocity and relaxation time of charge carriers in a conductor. A conductor of length $L$ is connected to a d.c. The source of emf ${}^{\prime }{E}^{\prime }$. If the length of the conductor is tripled by stretching it, keeping ${}^{\prime }{E}^{\prime }$ constant, explain how its drift velocity would be affected.

Answer 1

Drift velocity of an electron is given by:

$v_d=\frac{a\tau }{2}$

Electrostatic force is given by:

$ma=q{E}^{\prime }$

$v_d=\frac{q{E}^{\prime }\tau }{2m}$

where $E^{\prime }=\frac{E}{L}$

Now, length is tripled while keeping potential difference constant.

New electric field is given by $E^{\prime \prime }=\frac{E}{3L}=\frac{E^{\prime }}{3}$

Hence, $v_d^{\prime \prime }=\frac{v_d}{3}$

Hence, drift velocity will become 1/3rd.