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