Consider a sphere of radius R which carries a uniform charge density ρ. If a sphere of radius R/2 is carved out of it, as shown, the ratio (| E_A…

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