JEE Main 2024 — Electrostatics Question with Solution

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