Question

Expression for drift velocity in terms of relaxation time

Answer 1

Answer:

When conductor is subjected to an electric field E, each electron experience a force.

F=-eE

and acquires an acceleration

a = F/m = - eE/m -----(i)

Here m = mass of election, e = charge, E = electric field.

The average time difference between two consecutive collisions is known as relaxation time of election.

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Answer 2

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Consider a conductor of length 'l' and Area of cross section 'A', connected to a battery from electric field.

we know that, F = -eE ------> (1)

From newton's 2nd law

F= ma-------->(2)

from (1) and (2)

$ma = - eE \\ a = \frac { - aE}{m}$

where, 'e' is the charge of electron and 'm' is the mass of electron.Initially, the conductor is not applied to power supply then the average velocity of electron is 0.

therefore, Vo= 0

using the equations of motion,

$V = V_{0} + at \\ V_{d} = 0 + \frac{ - eE}{m} \: t \\ V _{d} = (\frac{ - Ee}{m} )t$

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