Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres σ₁/σ₂ is:
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Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres σ₁/σ₂ is:

G1 Physics · Accepted Answer

Step 1: Connected spheres reach equal potential: kq₁/R₁ = kq₂/R₂. Step 2: Thus q₁/q₂ = R₁/R₂. Step 3: Surface density σᵢ = qᵢ/(4πRᵢ²). Step 4: σ₁/σ₂ = (q₁/q₂)(R₂/R₁)² = R₂/R₁.