Two metal spheres having capacitances C₁ and C₂ hold some initial charges. They are brought into contact and subsequently separated. The final charges Q₁ and Q₂ on these spheres will satisfy

Step-by-step solution

When two conducting spheres are brought into contact, charge flows between them until their electrostatic potentials become equal. Let the common potential of the spheres after contact be V . The final charge on the first sphere is Q₁ = C₁ V . The final charge on the second sphere is Q₂ = C₂ V . Taking the ratio of the final charges, we get: Q₁ Q₂ = C₁ V C₂ V = C₁ C₂