Concentric spherical shells of radii $2$m, $4$m, and $8$ m carry uniform surface charge densities of $20 \: nC/m^2$, $ – 4 \: nC/m^2$ and $\rho_s$ respectively. The value of $\rho_s$ ($nC/m^2$) required to ensure that the electric flux density $\overrightarrow D$ = $\overrightarrow 0$ at radius $10$ m is ________