Q 12-01-103JEE MainJEE Main 2022 (27 Jul, Shift 1)Easy
A long cylindrical volume contains a uniformly distributed charge of density $\rho\ \text{C m}^{-3}$. The electric field inside the cylindrical volume at a distance $x = \dfrac{2\varepsilon_0}{\rho}$ m from its axis is ______ $\text{V m}^{-1}$.
Numerical value type. Enter your answer.
Answer: 1
Gauss's law on a coaxial cylinder of radius $x$ and length $l$:
$$E(2\pi xl) = \frac{\rho\pi x^2 l}{\varepsilon_0} \Rightarrow E = \frac{\rho x}{2\varepsilon_0}$$
$$E = \frac{\rho}{2\varepsilon_0}\cdot\frac{2\varepsilon_0}{\rho} = 1\ \text{V m}^{-1}$$
Solution by Sreeraj P, M.Sc Physics