A certain capacitor is fully charged by a battery, such that the positive plate holds a charge

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A certain capacitor is fully charged by a battery, such that the positive plate holds a charge \(+q\) and the negative plate holds a charge \(-q\). The plates of the capacitor are then pulled apart to twice their initial separation. Determine the new charge on the positive plate if \((a)\) the battery is kept attached to the capacitor as the separation is increased, and \((b)\) the battery is disconnected before the plate separation is increased.

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