The average drift velocity v_d of electrons in a metal is related to electric field E and collision time τ as

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BPSC AE Paper 5 (Electrical) 25 Mar 2022 Official Paper

Answer 1

Drift velocity:

It is the average velocity with which the electrons get drifted towards the positive terminal of the conductor in an electric field.

At any instant of time, the velocity acquired by the electrons with thermal velocity 'u₁' and acceleration 'a' is given by:

\(V_d = u_1+aτ\)..........(i)

where \(V_d = \) Drift velocity

u₁ = Average thermal velocity

a = Acceleration

τ = Relaxation time

The sum of averages of the thermal velocities of 'n' electrons in the conductor is 0.

∴ u1 = 0

The acceleration of an electron placed in an electric field is:

\(a = {F\over m_{e}}\)

\(a = {-Q_eE\over m_{e}}\).................(ii)

Putting the value of equation (ii) in (i), we get:

\(V_d = 0+aτ\)

\(V_d = -{Q_eE\tau\over m_{e}}\)