Electrostatics

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 ___________.