Electrostatics

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 _________.