JEE Main 2024 — 4 April, Shift 1 — Question 49

An infinite plane sheet of charge having uniform surface charge density $+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^{2}$ is placed on $\mathrm{x}-\mathrm{y}$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_{\mathrm{e}} \mathrm{C} / \mathrm{m}$ is placed at $\mathrm{z}=4 \mathrm{~m}$ plane and parallel to y -axis. If the magnitude values $\left|\sigma_{s}\right|=2\left|\lambda_{e}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{\mathrm{n}}: 1$. The value of $n$ is $\qquad$ .