Name: Meter Bridge
Uploaded: 2019-07-19
Duration: 7 min 2 s
Description: Measurement, by comparison, is always accurate. The video talks about a metre bridge device that helps us find the unknown resistance by comparing it with a...

Question

Obtain an expression for the drift velocity of an electron in a conductor.

Accepted Answer

The drift velocity is the average velocity acquired by the electrons inside the conductor when it is subjected to an electric field.

When a conductor is subjected to an electric field $E$ , each electron experience a force
$F = eE$ , where $e$ = charge on the electron. and acquires an acceleration of
$a = \frac{F}{m} = \frac{eE}{m_{e}}$ ..........................................................(1)

Where $m_{e}$ is the mass of the electron.
The average time difference between two consecutive collisions is known as the relaxation time of an electron is given by,

$τ = \frac{τ_{1} + τ_{2} + τ_{3} + τ_{4} + . . . . .}{n}$ , where $τ_{1}, τ_{2}, τ_{3},$ ... are the relaxation time of individual electrons and $n$ = the number of electrons.

In absence of any electric field, the electron inside the conductor are moving randomly in all directions. Hence their average thermal velocity of all electrons is zero.i.e.

$\frac{u_{1} + u_{2} + u_{3} + . . . . . .}{n} = 0$ .

The average velocity obtained by the electron in before it collides with another atom/electron is given by

$v = u + at = \frac{(u + u + u + . . .)}{n} + \frac{eE}{m_{e}} . τ = 0 + \frac{eE}{m} τ$ .

Hence the drift velocity= $- \frac{eE}{m_{e}} τ$ Minus sign indicates that the direction of the velocity is opposite to that of the electric field.

If $e$ is the charge on the electron, then total charge in the conductor is,

$q = Alne$ . Let the potential applied across the conductor= $V$ , then the electric field in magnitude = $\frac{V}{l}$ . The time taken by the free electrons to cover the conductor $t = \frac{l}{v_{d}}$ . Hence the current $I = \frac{q}{t} = \frac{Alne}{\frac{l}{v_{d}}} or I = {Anev}_{d}$ .

As $v_{d} = μ_{e} E$ we have $I = {Aneμ}_{e} E$ .

Putting the value of $v_{d}$ , we get,

$I = \frac{{Ane}^{2} τE}{m}$ . This is the expression of the current in the conductor.

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Obtain an expression for the drift velocity of an electron in a conductor.

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