A copper wire of radius $1 \mathrm{~mm}$ contains $10^{22}$ free electrons per cubic metre. The drift…

A copper wire of radius $1 \mathrm{~mm}$ contains $10^{22}$ free electrons per cubic metre. The drift velocity for free electrons when $10 \mathrm{~A}$ current flows through the wire will be (Given, charge on electron $=1.6 \times 10^{-19} \mathrm{C}$ )
  1. $\frac{6.25}{\pi} \mathrm{m} \mathrm{s}^{-1}$
  2. $\frac{6.25 \times 10^5}{\pi} \mathrm{m} \mathrm{s}^{-1}$
  3. $\frac{6.25 \times 10^4}{\pi} \mathrm{m} \mathrm{s}^{-1}$
  4. $\frac{6.25}{\pi} \times 10^3 \mathrm{~m} \mathrm{~s}^{-1}$

Solution

$V_d=\frac{i}{n e A}$ $\begin{aligned} & V_d=\frac{10}{10^{22} \times 1.6 \times 10^{-19} \times \pi\left(10^{-3}\right)^2} \\ & V_d=\frac{10}{1.6 \pi \times 10^{-3}} \\ & =\frac{6.25}{\pi} \times 10^3 \mathrm{~m} / \mathrm{s}\end{aligned}$

Asked in: NEET 2023 (Manipur)

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