A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is 10⁻⁷ J. The value of is __________. (combined capacitance of spheres is 200 pF)

Step-by-step solution

Initial energy of the charged sphere is given by: U_i = 1 2 C V^2 U_i = 1 2 100 10⁻¹² (100)^2 = 5 10⁻⁷ J When the identical uncharged sphere is brought in contact, the charge is shared equally and the common potential becomes: V' = V 2 = 50 V Final total energy of the two spheres is: U_f = 2 ( 1 2 C V'^2 ) = C V'^2 U_f = 100 10⁻¹² (50)^2 = 2.5 10⁻⁷ J Change in energy is the loss of energy during charge sharing: U = U_i - U_f = 5 10⁻⁷ - 2.5 10⁻⁷ = 2.5 10⁻⁷ J U = 5 2 10⁻⁷ J Comparing with 10⁻⁷ J, we get = 5 2 . Answe