Charge DistributionHardQuestion 31489
Question
Two conducting spheres of radii R₁ and R₂ connected by a long wire. In equilibrium, surface charge densities σ₁ and σ₂ satisfy:
- Aσ₁ = σ₂
- Bσ₁R₁ = σ₂R₂Correct
- Cσ₁/R₁ = σ₂/R₂
- Dσ₁R₁² = σ₂R₂²
Correct answer
σ₁R₁ = σ₂R₂
Explanation
Connected spheres: same potential V = kQ₁/R₁ = kQ₂/R₂. σ = Q/(4πR²). kσ×4πR²/R = const → σR = const → σ₁R₁ = σ₂R₂. Smaller sphere has higher σ (and higher E at surface).