Example 18-2 Electron Drift Speed in a Flashlight
In a large flashlight, the distance from the on-off switch to the light bulb is 10.0 cm. How long does it takes electrons
to drift this distance if the flashlight wires are made of copper, are 0.512 mm in radius, and carry a current of 1.00 A?
There are 8.49 * 1028 atoms in 1 m3 of copper, and one electron per copper atom is able to move freely through the metal.
Set Up
We’ll use Equation 18-3 to determine the
drift speed from the information given
about the number of mobile electrons,
the radius of the wire, and the current.
From this we’ll be able to find the drift
time by using the familiar relationship
between speed, distance, and time.
Solve
Calculate the drift speed of the electrons
in the wire.
Current and drift speed:
i = nAevdrift
1.00 A
(18-3)
+
switch
10.0 cm
+
Solve Equation 18-3 for the drift speed:
i
vdrift =
nAe
There is one mobile electron per atom and 8.49 * 1028 atoms>m3, so the
value of n is 8.49 * 1028 electrons>m3. The wire has a circular cross section
with radius r = 0.512 mm = 0.512 * 1023 m, so its cross-sectional area is
A = pr2 = p(0.512 * 1023 m)2 = 8.24 * 1027 m2
The magnitude of the charge per electron is e = 1.60 * 10-19 C>electron,
and the current is i = 1.00 A = 1.00 C>s. So the drift speed is
i
vdrift =
nAe
1.00 C>s
=
28
3
18.49 * 10 electrons>m 2 18.24 * 10-7 m2 2 11.60 * 10-19 C>electron2
= 8.94 * 10-5 m>s = 0.0894 mm>s
Then calculate how long it takes electrons to drift the distance from switch
to light bulb.
At this drift speed, the time it takes electrons to travel a distance d = 10.0 cm =
0.100 m from the flashlight on-off switch to the light bulb is
d
0.100 m
= 1.12 * 103 s
=
vdrift
8.94 * 10-5 m>s
1 min
b = 18.6 min
= 11.12 * 103 s2 a
60 s
t =
Reflect
The phrase “a snail’s pace” refers to something that moves very slowly. But an ordinary snail moves at about twice the
drift speed of electrons in this wire. The drift speed is so slow because electrons in the wire are continually colliding with
the copper atoms, which slows their progress tremendously. (More sophisticated physics shows that an electron in copper moves in random motion at an average speed of about 106 m>s, about 1010 times faster than the drift speed. In the
analogy we made earlier between electrons and a swarm of bees, you should think of the electrons in this wire as very
fast-moving bees within a swarm that’s drifting very, very slowly.)
At their slower-than-a-snail’s pace, it takes electrons more than a quarter of an hour to travel from the on-off switch
to the light bulb. Why, then, does the flashlight turn on immediately when you move the switch to the “on” position?
The explanation is that the wire is full of mobile electrons, and these electrons drift in response to the electric field in
the wire. With the switch in the off position, there is no electric field and so no drift. An electric field is only set up when
the switch is put in the on position, making a complete circuit like that shown in Figure 18-2. Changes in the electric
field propagate through the wire at close to the speed of light (3 * 108 m>s), so the field is set up throughout the circuit,
and the electrons begin to drift, in a tiny fraction of a second. That’s why the light comes on nearly instantaneously.