A conducting sphere of radius R carrying charge Q lies inside an uncharged conducting shell of radius 2 R . If they are joined by a metal wire, the amount of heat that will be produced is

Step-by-step solution

The capacitances of two are C₁=4 ₀ R and C₂=4 ₀(2 R) Initial energy =E_i= Q^2 2 C₁ Final energy =E_f= Q^2 2 C₂ Heat produced =E_i-E_f aligned & = Q^2 2 [ 1 4 ₀ R - 1 2 4 ₀ R ] & = 1 4 ₀ Q^2 2 R [1- 1 2 ] & = 1 4 ₀ Q^2 4 R aligned