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 ___________.