Velocity of free electrons in a wire

The free electrons in a metal have three distinct velocities associated with them:
(a) a random velocity ( about 10⁵ ms^-1)
(b) a velocity with which electrical energy is transferred along the wire (about 10⁸ms^-1)
(c) a drift velocity of the electrons as a whole when a current flows through the wire (this depends on the applied voltage but is usually a few mms^-1 for currents of a few amps in normal connecting leads).


The diagram in Figure 1 shows a simplified and enlarged view of a section of a wire carrying a current. The electrons are in random motion but if a potential difference is applied across the wire with the right hand end positive the free electrons drift slowly towards that end.

It is possible to measure the electron drift velocity (v) using the experiment outlined in the following Student Investigation.

Electron drift velocity

You can work out an equation for the electron drift velocity as follows:

Consider a wire of cross sectional area A and carrying a current I amps. Let the number of free electrons per unit volume be n and the drift velocity be v. (See Figure 3).


In one second an electron will have moved a distance v down the wire but since there are n electrons per unit volume the total number moving through this distance will be nAv. Therefore since the charge on an electron is e the current I (which is the charge moving past any point in the wire) is:


The table below shows some free electron concentrations

The electron steeplechase

When a current flows round a series circuit the current at any point in the circuit is the same. The same number of electrons flow past any point in the circuit every second - no electrons are lost. Although the number of electrons is always the same their energy gets less as they move round the circuit.

This energy appears as heat, light or magnetism in say an electrical heater, a light bulb or an electromagnet.



You can compare this energy loss with the change in energy of runners in a steeplechase. The energy loss of the athletes when going over the barriers represents the energy that electrons transfer when they pass through a resistor.