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

Question

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

Infinity Learn · Accepted Answer

Consider the smaller sphere having negative charge density.$$EA=O+K$$ρ$$.43$$$$π$$$$R23R/22=K$$ρ$$43$$$$π$$$$R2$$ $$EB=K$$ρ$$43$$$$π$$$$R3R2$$−Kρ$$43$$$$π$$$$R233R22$$                                       $$=K$$ρ$$43$$$$π$$R−Kρ$$43$$$$π$$$$R18$$                                       $$=K$$ρ$$43$$$$π$$$$17R18$$                                        ∴$$EAEB=K$$ρ$$43$$$$π$$$$R/2K$$ρ$$43$$$$π$$$$17R18$$                                         $$EAEB=1834$$

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

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