Two isolated metallic spheres of radii R and 2R are charged such that both have the same charge density . The spheres are then connected by a thin conducting wire. If the new charge density of the larger sphere is ₁ . The ratio ₁ to is

Step-by-step solution

Let the initial charge on the smaller sphere be Q₁ and on the larger sphere be Q₂ . Q₁ = (4 R^2) Q₂ = (4 (2R)^2) = 16 R^2 The total charge of the system is Q = Q₁ + Q₂ = 20 R^2 . When the spheres are connected by a conducting wire, charge flows until their potentials become equal. Let the new charges on the smaller and larger spheres be q₁ and q₂ respectively. Equating the potentials: 1 4 ₀ q₁ R = 1 4 ₀ q₂ 2R q₂ = 2q₁ By conservation of charge, q₁ + q₂ = Q . q₁ + 2q₁ = 20 R^2 3q₁ = 20 R^2 q₁ = 20 R^2 3 The new char