A sphere of capacitance 100 text{ pF} is char | vedclass

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(B) Initial energy $U_i = \frac{1}{2} C V^2 = \frac{1}{2} 	imes 100 	imes 10^{-12} 	imes (100)^2 = 0.5 	imes 10^{-6} 	ext{ J}$.After contact, cha

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$\frac{5}{2}$

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(B) Initial energy $U_i = \frac{1}{2} C V^2 = \frac{1}{2} 	imes 100 	imes 10^{-12} 	imes (100)^2 = 0.5 	imes 10^{-6} 	ext{ J}$.After contact, charge is shared equally because the spheres are identical $(C_1 = C_2 = 100 	ext{ pF})$.The common potential $V' = \frac{C_1 V + C_2(0)}{C_1 + C_2} = \frac{V}{2} = 50 	ext{ V}$.Total capacitance $C_{eq} = C_1 + C_2 = 200 	ext{ pF}$.Final energy $U_f = \frac{1}{2} C_{eq} (V')^2 = \frac{1}{2} 	imes 200 	imes 10^{-12} 	imes (50)^2 = 0.25 	imes 10^{-6} 	ext{ J}$.Energy loss $\Delta U = U_i - U_f = 0.5 	imes 10^{-6} - 0.25 	imes 10^{-6} = 0.25 	imes 10^{-6} 	ext{ J} = 2.5 	imes 10^{-7} 	ext{ J}$.Comparing with $\alpha 	imes 10^{-7} 	ext{ J}$, we get $\alpha = 2.5 = \frac{5}{2}$.

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