Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is σ′, the ratio σ′/σ is:
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Question

Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is σ′, the ratio σ′/σ is:

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G1 Physics · Accepted Answer

Initially Q₁ = 4πR²σ and Q₂ = 16πR²σ, so total charge = 20πR²σ. After connection, potentials are equal, so Q′₂ = 2Q′₁. Thus 3Q′₁ = 20πR²σ and Q′₂ = (40/3)πR²σ. Hence σ′ = Q′₂/[4π(2R)²] = (5/6)σ.