Q 12-03-196JEE MainJEE Main 2021 (24 Feb, Shift 2)Easy
A cylindrical wire of radius 0.5 mm and conductivity $5\times10^7\ \text{S m}^{-1}$ is subjected to an electric field of 10 mV m$^{-1}$. The expected value of current in the wire will be $x^3\pi$ mA. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 5
$J = \sigma E = 5\times10^7\times10^{-2} = 5\times10^5\ \text{A m}^{-2}$
$$I = J\pi r^2 = 5\times10^5\times\pi\times(0.5\times10^{-3})^2 = 0.125\pi\ \text{A} = 125\pi\ \text{mA} = 5^3\pi\ \text{mA}$$
So $x = 5$.
Solution by Sreeraj P, M.Sc Physics