Q 12-01-096JEE MainJEE Main 2022 (25 Jun, Shift 1)Easy
In the figure, a very large plane sheet of positive charge is shown. $P_1$ and $P_2$ are two points at distance $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitudes of electric fields $E_1$ and $E_2$ at $P_1$ and $P_2$ respectively are
Answer: (C) $E_1 = E_2 = \dfrac{\sigma}{2\varepsilon_0}$
For an infinite plane sheet of charge, Gauss's law with a cylindrical surface crossing the sheet gives $2EA = \dfrac{\sigma A}{\varepsilon_0}$, so
$$E = \frac{\sigma}{2\varepsilon_0}$$
independent of distance. Hence $E_1 = E_2 = \dfrac{\sigma}{2\varepsilon_0}$.
Solution by Sreeraj P, M.Sc Physics