📌 Derivation:

Step 1 — Equal Potential After Connecting:

When connected, both reach the same potential V:

kQ₁/R₁ = kQ₂/R₂

Q₁/Q₂ = R₁/R₂ ... (i)

Step 2 — Surface Charge Density:

σ = Q / (4πR²)

σ₁ = Q₁ / (4πR₁²)

σ₂ = Q₂ / (4πR₂²)

Step 3 — Ratio:

σ₁/σ₂ = (Q₁/R₁²) / (Q₂/R₂²)

= (Q₁/Q₂) × (R₂²/R₁²)

= (R₁/R₂) × (R₂²/R₁²)

┌─────────────────────┐

│ σ₁/σ₂ = R₂ / R₁ │

└─────────────────────┘

∴ <b>Surface charge density is inversely proportional to radius</b>.