In many computer keyboards the switches under the keys consist of small parallel-plate capacitors (see the figure attached). The key is attached to the upper plate, which is movable. When you push the key down, you push the upper plate toward the lower plate, and you alter the plate separation d and the capacitance. The capacitor is connected to an external circuit that maintains a constant potential difference V across the plates. The change of capacitance therefore sends a pulse of charge from the capacitor into the computer circuit. Suppose that the initial plate separation is 5.0 mm and the initial capacitance is 6.0 × 1013 F. The final plate separation (with the key fully depressed) is 0.20 mm. The constant potential difference is 8.0 V. What is the change in capacitance when you depress the key? What is the amount of electric charge that flows out of the capacitor into the computer circuit? What happens to the energy stored in the capacitor?

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