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