Question

Estimate the average drift of conduction electrons in a copper wire of cross-sectional area $2.5 \times {10^{ - 7}}{m^2}$ carrying a current of $2.7A$ . Assume the density of conduction electrons to be $9 \times {10^{28}}{m^{ - 3}}$

Answer 1

Hint Using the formula for the current in a wire in the terms of the drift velocity, we can calculate the drift velocity. By substituting the values that are given in the question, we will get the answer.

Formula Used: In this solution we will be using the following formula,
$\Rightarrow I = Anq{v_d}$
where $I$ is the current, $A$ is the area of cross-section, $n$ is the number density, $q$ is the charge and ${v_d}$ is the drift velocity.

Complete step by step answer
In this problem, we need to find the drift velocity of the electrons. Now, the current in a circuit is given by the formula,
$\Rightarrow I = Anq{v_d}$
Now we can arrange this formula to get the drift velocity as,
$\Rightarrow {v_d} = \dfrac{I}{{Anq}}$
Here we are given the current in the wire as, $I = 2.7A$ . The number density of the electrons in the copper wire is $n = 9 \times {10^{28}}{m^{ - 3}}$ and the area of cross-section of the wire is $A = 2.5 \times {10^{ - 7}}{m^2}$ . Now in this case we are calculating the drift velocity for the electrons. So we will be considering the charge of the electrons. Therefore we have $q = 1.6 \times {10^{ - 19}}C$ .
Now substituting the values in the equation we get,
$\Rightarrow {v_d} = \dfrac{{2.7}}{{2.5 \times {{10}^{ - 7}} \times 9 \times {{10}^{28}} \times 1.6 \times {{10}^{ - 19}}}}$
On calculating the denominator we get
$\Rightarrow {v_d} = \dfrac{{2.7}}{{3600}}$
On doing the division we get the value as,
$\Rightarrow {v_d} = 7.5 \times {10^{ - 4}}m/s$
This is the average drift of conduction electrons in a copper wire.

Note
The drift velocity is the average velocity that is attained by charged particles such as electrons in a material due to the presence of an electric field. The magnitude of the drift velocity is proportional to the current and also to the magnitude of the electric field.