Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2} \frac{R}{2}$ is carved out of it, as shown, the ratio $\frac{\left|\vec{E}_A\right|}{\left|\vec{E}_B\right|}$ of magnitude of electric field $\overrightarrow{\mathrm{E}}_A$ and $\overrightarrow{\mathrm{E}}_B$, respectively, at points $A$ and $B$ due to the remaining portion is: