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 → E B → of magnitude of electric field E A → and E B → , respectively, at points A and B due to the remaining portion is:

Step-by-step solution

E = ρ r 3 ε 0 E A = - ρ R 2 3 ε 0 E A = ρ R 6 ε 0 Electric filed at point B = E B = E 1 A + E 2 A E 1 A = Electric Filed Due to solid sphere of radius R at point B = ρ R 3 ε 0 E 2 A = Electric Filed Due to solid sphere of radius R 2 (which having charge density – ρ ) at point B = - K Q ' × 4 9 R 2 = - ρ R 54 ε 0 E B = E 1 A + E 2 A = ρ R 3 ε 0 - ρ R 54 ε 0 = 17 ρ R 54 ε 0 E A E B = 9 17