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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. source of emf E. If the length of the conductor is tripled by stretching it, keeping E constant, explain how its drift velocity would be affected.

Solution:

Drift velocity of an electron is given by: vd = aτ/2
Electrostatic force is given by: ma = qE'
vd = qE'τ/2m
where E' = E/L
Now, length is tripled while keeping potential difference constant.
New electric field is given by E'' = E/3L = E'/3
Hence, v''d = vd/3
Hence, drift velocity will become 1/3rd.