Question

A copper wire with a cross section area of $ 2 \times {10^{ - 6}}{m^2} $ and has a free electron density equal to $ 5 \times {10^{22}}/c{m^2} $. If this wire carries a current of 16 A, the drift velocity of the electron is?
(A) 1 m/s
(B) $ 0.1m/s $
(C) $ 0.01m/s $
(D) $ 0.001m/s $
(E) $ 0.00001m/s $

Answer 1

Hint: The current flowing through a conductor is proportional to the drift velocity, the cross sectional area of the conductor, the charge of the electron and finally the free electron density of the material. When current and all other quantities are known, the drift velocity can be calculated. We should use all units in SI.

Formula used: In this solution we will be using the following formula;
 $ I = nevA $, where $ I $ is the current flowing through a conductor, $ n $ is the free electron density of the material, is the charge of an electron, $ v $ is the drift velocity, and $ A $ is the cross section area of the conductor.

Complete step by step answer
Whenever for a conductive material a voltage is applied across the ends of a conductive material, the electrons are mobilized, and directed toward the opposite direction of the electric field (because electrons are negative charge). The current considered to flow in the conductor is as a result of the movement of these electrons. Hence, the higher the speed of these electrons, the higher is the current. The velocities of these electrons are called drift velocity.
In general, the current is given as,
 $ I = nevA $, where, $ n $ is the free electron density of the material, is the charge of an electron, $ v $ is the drift velocity, and $ A $ is the cross section area of the conductor.
Hence, by inserting all known values, we have
 $ 16 = \left( {5 \times {{10}^{22}} \times {{10}^4}} \right)\left( {1.6 \times {{10}^{ - 19}}} \right)v\left( {2 \times {{10}^{ - 6}}} \right) $ (since $ 1{m^2} = {10^{ - 4}}c{m^2} $ )
By computation,
 $ 16 = 160v $
Thus, making $ v $ subject
 $ v = \dfrac{{16}}{{160}} = 0.1m/s $
Hence, the correct option is B.

Note
We can see that the drift velocity is very low, even for such a high current. The fact that large current can flow through a conductor is due to the large free electron density of the conductive material.
Also, in actuality, this is not the speed of electricity. The drift velocity above for example predicts that it would take 10 seconds for an electron to flow from one end of a mere 1 metre conductor to another. This is however not the case, as electricity is detected almost instantaneously even across hundreds of kilometres. This is because as soon as one electron enters the conductor from one end, its presence ejects another electron from the other end almost immediately even though the electron itself is still within the conductor.