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).
electron
metal ion
Figure 1
electron drift
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.
Student Investigation
It is not possible to measure the electron drift velocity in a
metal directly but an idea of its value can be found by
measuring the drift velocity of ions in a liquid.
A piece of filter paper should be clipped to a microscope
slide and then soaked with a dilute solution of ammonium
hydroxide. A crystal of potassium permanganate should
be put on the paper and a voltage applied between the
two clips. The coloured manganate ions can be seen to
move and their velocity can be measured. (Figure 2).
Record the variation of drift velocity for voltages between
50V and 250V.
DANGER: take care not to touch the
H.T terminals during the experiment.
filter paper
V
crystal
microscope slide
Figure 2
Student Investigation
Devise and carry out an experiment to investigate the conduction of electricity along pencil lines
drawn on a sheet of paper
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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).
v
A
e
e
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:
Current (I) = nAve
The table below shows some free electron concentrations
Metal
Lithium
Sodium
Silver
Copper
Free electron concentration (m-3) (at 300 K)
4.7x1028
2.7x1028
5.9x1028
8.5x1028
Example problems
1. Calculate the drift velocity of electrons in a copper wire of cross sectional area 2x10 -7 m2
(0.5mm diameter) carrying a current of 0.5A. (n = 8.5x1028)
v = I/nAe = 0.5 /[8.5x1028x2x10-7x1.6x10-19] = 1.84x10-4ms-1 = 0.184mms-1
2. A motorist switches on their headlights. If the distance along the copper connecting wires
between the car battery and one of the lights is 1.5 m what is the average time that an individual
electron will take to drift between the battery and the light? Take the current in the wire to be 3A,
and the cross sectional area of the wire to be 3x10-7 m2.
v = I/nAe = 3 /[8.5x1028x3x10-7x1.6x10-19] = 7.4x10-4ms-1 = 0.74 mms-1
Therefore time taken = 1.5/7.4x10-4 = 4080 s = 1.13 hours
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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.
Figure 3
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.
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