Mean drift velocity

In a nutshell

The number density is the number of free electrons per unit volume of a material. Conductors have a high number density and insulators have a very low number density with semiconductors in between. The mean drift velocity is the average speed at which electrons move towards the positive terminal.

Equations

Description	equation
Electric current	$I=Anev$

Constants

constant	symbol	value
$elementary\ charge$	$e$	$1.6\times10^{-19}\ C$

Variable definitions

quantity name	symbol	derived units	si base units
$current$	$I$	$A$	$A$
$area$	$A$	$m^2$	$m^2$
$number\ density$	$n$	$m^{-3}$	$m^{-3}$
$mean\ drift\ velocity$	$v$	$m\ s^{-1}$	$m \ s^{-1}$

Conductors, semiconductors and insulators

Materials can be classified into the following three groups.

Conductors	Materials that facilitate the flow of electrons and have a high conductivity.
Insulators	Materials that have a very low conductivity as they prevent the flow of energy between two objects.
Semiconductors	Materials that have a moderate conductivity falling between conductors and insulators.

These three types of material can be classified according to their number density. The number density is the number of free electrons per unit volume. The higher the number density, the more conductive a material is as it has more free electrons that can carry charge.

Mean drift velocity

When electrons flow through a wire they move randomly but tend to drift towards the positive terminal, the speed of this drift is called the mean drift velocity. Since current is the rate of flow of electrons it is possible to find it by simply knowing how many electrons cross a section of the wire per second, hence we can use the formula:

$I=Anev$

Exam tip: This is the only equation with mean drift velocity, if you have a question on this topic chances are you will need it!

The number density multiplied by the volume gives the total number of electrons and volume per second can be written as area times velocity, hence you can find the current with this formula.

Physics; Current and charge; KS5 Year 12; Mean drift velocity

Note: The mean drift velocity is not the speed of individual electrons but the average speed of all the electrons in the direction of the positive terminal.

Example

A copper wire has a cross sectional area of $4\times10^{-8}\ m^{2}$ and a number density $8.5\times10^{28}\ m^{-3}$ . Calculate the current when electrons flow through it with a mean drift velocity of $1.8\times10^{-3}\ m\ s^{-1}$ .

Firstly, write down all the known values:

$\begin{aligned}A&=4\times10^{-8}\ m^2 \\n&=8.5\times10^{28}\ m^{-3} \\v&=1.8\times10^{-3}\ m\ s^{-1}\end{aligned}$ 

Next, write down the equation for current:

$I=Anev$ 

Substitute all the values into the equation:

$I=4\times10^{-8}\times8.5\times10^{28}\times1.6\times10^{-19}\times1.8\times10^{-3}$ 

Calculate the current:

$I=0.98\ A$ 

The current flowing through the wire is $\underline{0.98\ A}$ .