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# The drift velocity of the electron in a copper wire of length 2m under the application of a potential difference of 200 V is $0.5m{{s}^{-1}}$. Their mobility ($in\,m{{s}^{-2}}{{V}^{-1}}{{s}^{-1}}$)(A) $5\times {{10}^{-3}}$(B) $2.5\times {{10}^{-2}}$(C) $5\times {{10}^{2}}$(D) ${{10}^{-3}}$

Last updated date: 21st Apr 2024
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Hint: We know that drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero. Drift velocity is independent of time. Drift velocity is the reason due to which current flows inside a conductor. In the derivation of the equation of drift velocity, we can see that acceleration a is constant and relaxation time. The charge of the electrons in a few cm of copper wire is very large. For instance, it is similar to the total charge of a D-cell. In order to convey the current, they have only to move very slowly indeed. Based on this concept we have to answer this question.

At first let us mention the values that are mentioned in the question:
Length, d = 2m
Now the Potential difference, V = 200V
Now we have to find the value of mobility. So, let us write the formula of mobility as:
Mobility, $\mu =\dfrac{{{v}_{d}}}{E}$
$=\dfrac{{{v}_{d}}\times d}{V}\,$
Now we have to put the values in the above expression:
$=\dfrac{0.5}{200}\times 2\,$
On evaluation we get that:
$=\dfrac{0.5}{100}=5\times {{10}^{-3}}{{m}^{2}}{{V}^{-1}}{{s}^{-1}}$

Hence, the correct answer is Option A.

Note: We should know that drift velocity is important because the current flowing in a conductor is directly proportional to the drift velocity of electrons. The electrons inside a conductor move with random velocities in random directions unless an electric field is applied to the conductor. Drift velocity is always due to minority charge carriers. However, thermal velocity or agitation is due to movement of free charge carriers and ions and hence it is always greater than drift velocity.
Thus, we say that drift velocity is defined as the average velocity attained by the particles (electrons) of a given material due to an electric field that is proportional to current.