Drift Velocity and Current
Electric current is the flow of charge. The charges that actually flow are the electrons.
The ions can only vibrate about their fixed positions, but the electrons are free to move randomly from one ion to the next. They are known as “free” electrons. All metals have a structure like this.
When a circuit is made, the “free” electrons are repelled by the negative terminal and attracted to the positive. The electrons are still moving in a random way, but in addition to this they all move slowly in the same direction through the wire with a drift velocity .
The better the conductor the more “free” electrons there are.
X
Is there a relationship between the current in a wire and the drift velocity of the electrons?
Volume of conductor = A l
Number of “free” electrons: = n A l
Total charge, Q, of “free” electrons = n A l e l
If Q = I t then I = Q/t = n A l e / t
But v = l / t so I = n A v e
Example questions:
1.
Zinc contains 1 x 10
29
“free” electrons per m
3
. What is the drift velocity of electrons in a copper wire of cross sectional area 0.25mm
2
carrying a current of 0.4A?
2.
(a) If the density of copper is 9.0 x 10
3 kg m
-3
and 63.5 kg of copper contains 6.0 x 10
26 atoms, find the number of “free” electrons per cubic metre of copper assuming that each copper atom has one “free” electron.
(b) How many “free” electrons will there be in 1.0m of copper wire of cross sectional area
1.0 x 10
-6 m
2
(i.e. 1.0 mm
2
)?
(c) Taking the charge on an electron to be 1.6 x 10
-19
C, what is the total charge of the “free” electrons per metre of wire?
(d) Assuming that the “free” electrons are responsible for conduction, how long will the charge in (c) take to travel 1m when a current of 2.0A flows?
(e) What is the drift velocity of the “free” electrons?