Question

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

Answer 1

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
$x =5$