An isolated conducting sphere of radius R is given a charge, resulting in a stored electrostatic energy U . A concentric uncharged conducting spherical shell of radius 3R is then placed around it and connected to earth. The new electrostatic energy of the system is:

Step-by-step solution

The initial capacitance of the isolated conducting sphere is C₁ = 4 ₀ R . Let the charge on the sphere be Q . The initial electrostatic energy is: U = Q^2 2C₁ When the concentric uncharged conducting spherical shell of radius 3R is placed around it and earthed, the inner sphere remains isolated, so its charge Q is conserved. The new capacitance of the system (a spherical capacitor with the outer shell earthed) is: C₂ = 4 ₀ (R)(3R) 3R - R = 4 ₀ (3R^2) 2R = 3 2 (4 ₀ R) = 3 2 C₁ The new electrostatic energy of the sys