NEET 2021 · PhysicsPrevious Year Question
Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. Then the ratio of the surface charge densities of the spheres (σ₁/σ₂) is
Answer: (D) R₂/R₁. Answer: (d) Solution: When connected by a wire, the two conductors reach a common potential: V = kQ₁/R₁ = kQ₂/R₂ → Q₁/Q₂ = R₁/R₂ Surface charge density: σ = Q/(4πR²).
- A.(R₁/R₂)²
- B.R₂²/R₁²
- C.R₁/R₂
- D.R₂/R₁✓
Correct Answer
(D) R₂/R₁
Solution & Explanation
Answer: (d) Solution: When connected by a wire, the two conductors reach a common potential: V = kQ₁/R₁ = kQ₂/R₂ → Q₁/Q₂ = R₁/R₂ Surface charge density: σ = Q/(4πR²). σ₁/σ₂ = (Q₁/R₁²)/(Q₂/R₂²) = (Q₁/Q₂)·(R₂²/R₁²) = (R₁/R₂)·(R₂²/R₁²) = R₂/R₁. So σ ∝ 1/R, giving σ₁/σ₂ = R₂/R₁.
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