Question

Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0\times {{10}^{-7}}{{m}^{2}}$ carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0\times {{10}^{3}}kg{{m}^{-3}}$

Answer 1

In physics we use drift velocity for charge particles, Drift velocity is the same as that of average velocity, the only difference is that drift velocity is used for charged particles. For example, electrons travel randomly with different speeds but when an electric field is applied, they travel with an average velocity known as drift velocity.

Complete step-by-step solution:
In this question we have been given with few quantities
cross-sectional area (A) = $1.0\times {{10}^{-7}}{{m}^{2}}$
Current (I) = 1.5 A
density of copper ($\rho$) = $9.0\times {{10}^{3}}kg{{m}^{-3}}$
There are also some quantities that we are aware of such as
Atomic mass of copper = 63.5 amu
Molar mass of copper (M) = $63.5\times {{10}^{-3}}kg$
Now as per the question, we need to find out the drift velocity of conduction electron
Number of copper atoms per unit volume can be given as
$N=\rho \dfrac{{{N}_{A}}}{M}$
$N=9\times {{10}^{3}}\times \dfrac{6.023\times {{10}^{23}}}{63.5\times {{10}^{-3}}}$
$N=8.54\times {{10}^{28}}$
We know that one copper atom contributes to one conduction electron, so this means that number of conduction electron per unit volume can be given as
n = $N=8.54\times {{10}^{28}}$
Now the relation between current and drift velocity can be given by
$I=AneV{}_{d}$
Where “I” is the current “A” is the area “n” is the number of conduction electrons and ${{V}_{d}}$ is the drift velocity
Putting the values in above equation, we get
$1.5={{10}^{-7}}\times 8.54\times {{10}^{28}}\times 1.6\times {{10}^{-19}}\times {{V}_{d}}$
${{V}_{d}}=1.1\times {{10}^{-3}}m{{s}^{-1}}$
Hence, we can say that for the above question the drift velocity of the electron will be ${{V}_{d}}=1.1\times {{10}^{-3}}m{{s}^{-1}}$

Note: In this question we have assumed that we know some of the quantities that are required to solve this question and are constant, most of the time these quantities are given in the question, but if not given then we should remember these quantities are they are required in such type of questions.