(a) The energy stored in the capacitor can be calculated as follows:
b) Let's first calculate the charge stored on the capacitor:
Let's find the new capacitance of the capacitor. The capacitance can be calculated as follows:
From the conditions of the question we know that the separation between the plates of the capacitor is doubled, therefore, the new capacitance will be:
Finally, we can find the energy stored in the capacitor:
As we can see from the calculations, when the battery is disconnected from the capacitor and the separation between plates is doubled, capacitance is halved. As a result, the energy stored in the capacitor increases.
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