Consider a sphere of radius R which carries a uniform charge density 'ρ' . If a sphere of radius R2  is carved out of it, as shown. The ratio  EAEB of magnitude of electric field E→A  and E→B, respectively at points A and B due to the remaining portion is

Consider the smaller sphere having negative charge density.EA=O+Kρ.43πR23R/22=Kρ43πR2 EB=Kρ43πR3R2−Kρ43πR233R22                                       =Kρ43πR−Kρ43πR18                                       =Kρ43π17R18                                        ∴EAEB=Kρ43πR/2Kρ43π17R18                                         EAEB=1834