A conducting sphere of radius R carries a total charge Q . It is connected by a thin conducting wire to an initially uncharged conducting sphere of radius 3R . After electrostatic equilibrium is reached, what is the surface charge density of the smaller sphere?

Step-by-step solution

Let the final charges on the smaller and larger spheres be q₁ and q₂ respectively. When connected by a wire, their potentials become equal: V₁ = V₂ . k q₁ R = k q₂ 3R q₂ = 3q₁ By conservation of charge, the total charge remains Q : q₁ + q₂ = Q q₁ + 3q₁ = Q 4q₁ = Q q₁ = Q 4 The surface charge density of the smaller sphere is: ₁ = q₁ 4 R^2 = Q 4 4 R^2 = Q 16 R^2 Answer: Q 16 R^2