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Charge passing through a conductor of cross-section area $A=0.3 \mathrm{~m}^2$ is given by $q=3 t^2+5 t+2$ in coulomb, where $t$ is in second. What is the value of drift velocity at $t=2 \mathrm{~s}$ ? (Given, $n=2 \times 10^{25} / \mathrm{m}^3$ )
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The correct answer is:
$1.77 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
$A=0.3 \mathrm{~m}^2$
$n=2 \times 10^{25} / \mathrm{m}^3$
$q=3 t^2+5 t+2$
$i=\frac{d q}{d t}=6 t+5=17$
$i=n e A v_d$
Drift velocity,
$v_d=\frac{i}{n e A}$
$=\frac{17}{2 \times 10^{25} \times 1.6 \times 10^{-19} \times 0.3}$
$=\frac{17}{0.96 \times 10^6}$
$=1.77 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
$n=2 \times 10^{25} / \mathrm{m}^3$
$q=3 t^2+5 t+2$
$i=\frac{d q}{d t}=6 t+5=17$
$i=n e A v_d$
Drift velocity,
$v_d=\frac{i}{n e A}$
$=\frac{17}{2 \times 10^{25} \times 1.6 \times 10^{-19} \times 0.3}$
$=\frac{17}{0.96 \times 10^6}$
$=1.77 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
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