Question:
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 $\mathrm{x}^{3} \pi \mathrm{mA}$.
The value of $x$ is
Solution:
(5)
We know that $\mathbf{J}=\sigma \mathrm{E}$
$\Rightarrow \mathrm{J}=5 \times 10^{7} \times 10 \times 10^{-3}$
$\Rightarrow \mathrm{J}=50 \times 10^{4} \mathrm{~A} / \mathrm{m}^{2}$
Currentflowing $I=J \times \pi R^{2}$
$I=50 \times 10^{4} \times \pi\left(0.5 \times 10^{-3}\right)^{2}$
$I=5 \times 10^{4} \times \pi \times 0.25 \times 10^{-6}$
$I=125 \times 10^{-3} \pi$
$X=5$