JEE Main 2023 — Electrostatics Question with Solution

A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5\mathrm{m}$$ distance from each other. Points 'P' and 'Q' are at $$\frac{3}{\pi }$$ m and $$\frac{4}{\pi }$$ m perpendicular distances from line charge towards sheet charge, respectively. '$${\mathrm{E}}_{\mathrm{P}}$$' and '$${\mathrm{E}}_{\mathrm{Q}}$$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $$\frac{E_p}{E_0}=\frac{4}{a}$$ for $$2|\sigma |=|\lambda |$$, then the value of $$a$$ is ___________.