Electrical current is the rate at which charged particles flow, usually through a conductor. The drift velocity is the average velocity at which these free charges (typically electrons) move with.
The atoms in conductors have free charges that move randomly until they are in an electric field. An electric field causes them to drift in a particular direction. In the case of electrons (a negatively charged particle) they drift in the direction opposite to that of the electric field.
As conductors have a large number of free charges electrical signals can travel through wires at high speeds. However, the speed of the individual free charges is relatively slow.
The reason for this is that they can only move a short distance before hitting an atom or other free charge within the metal.
Drift Velocity Equation
Most wires are made of copper and the charged particles within copper are electrons with a charge of -1.6×10-19C (e). The diagram below shows part of a copper wire with a small section highlighted in blue:
The blue section has a length of d and cross sectional area A. We can use this section of wire to find an equation for drift velocity in terms of current.
Charge
Firstly we need to consider the number of free charges per unit volume (n) in the blue section of the wire. This value varies from metal to metal because it is dependent on the number of free electrons as well as the density of atoms in the metal. Copper has about one free electron (conduction electron) per atom.
The volume of the blue section is equal to the length (d) multiplied by the cross sectional area (A): V = Ad. Multiplying this by the number of free charges per unit volume (n) gives the total number of free electrons – nAd.
From this, we can calculate the total charge of the conduction electrons in this section by multiplying by the charge of an electron (e). This gives:
Time
Now we have the total free charge in the blue section we need to consider the velocity of the electrons. For an electron to travel the distance (d) of the blue section the drift velocity is given by: . This can be rearranged to make time the subject giving:
Current
The current (I) along the wire is given by:
By substituting the total charge of the section and the time for an electron to travel the length of the section into this equation we get the following equation:
Drift Velocity
Rearranging for drift velocity we get:
Worked Examples
Use e=1.6×10-19C for both questions.
Example 1
An electron in a copper wire has a drift velocity of 5×10-4 ms-1 and the current flowing through the wire is 10A. Calculate the cross sectional area of the wire given that n = 8.5×1028 electrons/m3.
Example 2
A copper wire with a radius of 8×10-4m has a current of 5A. Calculate the drift velocity of an electron in this wire given that n = 8.5×1028 electrons/m3.
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