### How much work is done by external agent acting on dielectric

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Q. A dielectric-filled parallel-plate capacitor has plate area of 30cm^2 and plate separation of 5mm. The capacitor is connected to a battery that creates a constant voltage of 10V. The dielectric constant is 3. All through the problem, use epsilon_0 = 8.85×10^-12 (C^2/N * m^2).

1) Find out the energy U_1 of the dielectric-filled capacitor. (In J)

2) The dielectric plate is now slowly pulled out of capacitor that remains connected to the battery. Find the energy U_2 of the capacitor at the moment when the capacitor is half-filled with the dielectric (in J)

3) The capacitor is now disconnected from the battery, and the dielectric plate is then slowly removed the rest of the way out of the capacitor. Find out the new energy of the capacitor, U_3.

4) In the method of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on dielectric?

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