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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 _________.
Option: 1 5
Option: 2 10
Option: 3 15
Option: 4 20

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\begin{array}{l} \text { Conductivity } \sigma=5 \times 10^{7} \mathrm{~S} / \mathrm{m} \\ \text { Radius } \mathrm{r}=0.5 \mathrm{~mm}=5 \times 10^{-4} \mathrm{~m} \\ \mathrm{E}=10 \times 10^{-3} \frac{\mathrm{V}}{\mathrm{m}} \\ As \ \mathrm{J}=\sigma \mathrm{E}=10 \times 10^{-3} \times 5 \times 10^{7} \\ So \ \mathrm{~J}=5 \times 10^{5} \\ \Rightarrow J=\frac{i}{A}=5 \times 10^{5} \\ \Rightarrow \mathrm{i}=5 \times 10^{5} \times \pi \mathrm{r}^{2} \\ \Rightarrow i=5 \times 10^{5} \times \pi \times\left(5 \times 10^{-4}\right)^{2} =125 \pi \times 10^{-3} \mathrm{Amp} \\ \Rightarrow \mathrm{i}=125 \pi \mathrm{mA} \\ \therefore \mathrm{x}=5 \end{array}

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