ρ₀/(3ε₀)(r³ - r²/4R)
ρ₀/(12ε₀)(r³ - r²/4R)
ρ₀/(4ε₀)(r³ - r²/4R)
ρ₀/(ε₀)(r³ - r²/4R)
Answer is B. Electric field at the internal point r is the sum of fields due to outer and inner spheres. However, the contribution due to the outer part is zero. For the inner part, consider a shell of thickness dr' at a distance of r' from the center of the sphere. Therefore, charge contained in it dq = 4πr'²dr'ρ₀(1 - r'/R). Or, Electric field dE is dE = 1/(4πε₀)r² * 4πr'²dr'ρ₀(1 - r'/R). Integrating above, we get E = ρ₀/(ε₀r²) ∫₀ʳ (r'² - r'³/R)dr' E = ρ₀/(ε₀)(r³/3 - r⁴/(4R))