As the separation between the plate increases, the capacitance decreases even if the charge is constant. The electric field between the plate is constant.
If there is vacuum between the plates of the capacitor then the plates of the capacitor will attract each other and they will stick to each other. Hence a support is needed to keep the plates away from each other.
In the process to separate the plates apart from each other, the external positive work done becomes the additional electric potential energy which is stored in the capacitor. The electric potential energy which is stored in the capacitor is changed from the chemical energy
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