A solid non-conducting sphere has volume charge density ρ(r) = Ar/R. If the electric field at distance R/2 from the centre is E = 2R/ε₀ N C⁻¹, find A/16.
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A solid non-conducting sphere has volume charge density ρ(r) = Ar/R. If the electric field at distance R/2 from the centre is E = 2R/ε₀ N C⁻¹, find A/16.

G1 Physics · Accepted Answer

For r < R, Q(r) = 4π∫₀ʳ [Ar'/R]r'²dr' = πAr⁴/R. At r = R/2, Q = πAR³/16. Hence E = Q/[4πε₀(R/2)²] = AR/(16ε₀). Given E = 2R/ε₀, A = 32 and A/16 = 2. Correct answer: A.