A cylindrical wire of radius $0.5 \,mm$ and conductivity $5 \times 10^{7}\, S / m$ is subjected to an electric field of $10 \,mV / m .$ The expected value of current in the wire will be $x ^{3} \,\pi mA$. The value of $x$ is ......
JEE MAIN 2021, Medium
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Conductivity $\sigma=5 \times 10^{7} \,S / m$
Radius $r =0.5 \,mm =5 \times 10^{-4}\, m$
$E =10 \times 10^{-3}\, \frac{ V }{ m }$
$J =\sigma E =10 \times 10^{-3} \times 5 \times 10^{7}$
$J =5 \times 10^{5}$
$\frac{ i }{ A }=5 \times 10^{5}$
$i =5 \times 10^{5} \times \pi r ^{2}$
$=5 \times 10^{5} \times \pi \times\left(5 \times 10^{-4}\right)^{2}$
$=125 \pi \times 10^{-3} \,Amp$
$i=125 \pi \, mA$
$x=5$
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