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The parallel plates in a capacitor, with a plate area of \( 8.50 \mathrm{~cm}^{2} \) and an air-filled separation of \( 8.00 \mathrm{~mm} \), are charged by a \( 16.0 \mathrm{~V} \) battery. They are then disconnected from the battery and pushed together (without discharge) to a separation of \( 3.00 \mathrm{~mm} \). Neglecting fringing, find (a) the potential difference between the plates, (b) the initial stored energy, (c) the final stored energy, and (d) the (negative) work in pushing them together.
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