Mean Drift Velocity

Physics: Cambridge International A Level, topic 12.1.2

Current Flowing Through a Wire

You need to be able to derive the equation for the current flowing through a wire in terms of its cross-sectional area and the mean drift velocity of electrons flowing through it.

Electrons in a wire

If we take a small section of a wire with electrons flowing through it.
The wire has a cross-sectional area $A$ , and length $L$ .
Let $n$ be equal to the number density of electrons in the wire, which is the number of electrons per unit volume.
We can then write the total change in charge as the electrons pass through the section of the wire as:
$\Delta Q = A \times L \times n \times q$

Electrons in a wire

Mean drift velocity

Substituting this into the equation for current, we have:
$I = \frac{ALnq}{\Delta t}$
We can rewrite this as:
$I = Anqv$
Where $v=\frac{L}{\Delta t}$ is called the mean drift velocity of the electrons.

Mean Drift Velocity

Mean drift velocity is the average distance travelled by a charge carrier per unit time.

Movement of charges

An electron moving through a wire has a chaotic, zigzag path, but with a migration in a particular direction if a potential difference is applied to the wire.

Mean drift velocity

With a current of a few amps, the average or mean drift velocity of electrons will be of the order of 0.3 mm per second. A high current is possible because there are very many, closely packed charges.

Test yourself on Mean Drift Velocity

What is the number density of 1 × 10³⁵ electrons in a wire of length 3 mm and cross sectional area of 1 mm²?
What is the equation for the current in a wire?

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