A system consists of uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density ρ = α/r , where a is a positive constant and r is the distance from the centre of the sphere. The charge of the sphere for which electric field intensity E outside the sphere is independent of r is
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Question

A system consists of uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density ρ = α/r , where a is a positive constant and r is the distance from the centre of the sphere. The charge of the sphere for which electric field intensity E outside the sphere is independent of r is

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G1 Physics · Accepted Answer

Step 1: Use superposition, 𝐄 = Σ[1/(4πε₀)] qᵢ 𝐫ᵢ/rᵢ³, or the appropriate continuous-distribution integral. Step 2: Resolve components and exploit symmetry to cancel components. Step 3: Add the surviving components and compare with the choices. Final: C: 2 paR².