Q 12-02-038JEE MainJEE Main 2026 (6 Apr, Shift 2)Medium
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 $\alpha \times 10^{-7}$ J. The value of $\alpha$ is ______. (combined capacitance of spheres is $200$ pF)
Answer: (B) $\dfrac{5}{2}$
Initially $U_1 = \dfrac{1}{2}CV^2 = \dfrac{1}{2} \times 10^{-10} \times 10^4 = 5 \times 10^{-7}$ J, with $Q = CV = 10^{-8}$ C.
After contact the same charge is on $200$ pF: $U_2 = \dfrac{Q^2}{2C'} = \dfrac{10^{-16}}{4 \times 10^{-10}} = 2.5 \times 10^{-7}$ J.
Change in magnitude $= 2.5 \times 10^{-7}$ J, so $\alpha = \dfrac{5}{2}$.
Solution by Sreeraj P, M.Sc Physics