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An air-filled parallel-plate capacitor has plate area A andplate separation d. The capacitor is connected...

An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V.

A) Find the energy U_0 stored in the capacitor. Express your answer in terms of A, d, V, and ϵ_0.

B) The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d. Find the new energy U_1 of the capacitor after this process. Express your answer in terms of A, d, V, and ϵ_0.

C) The capacitor is now reconnected to the battery, and the plate separation is restored to d. A dielectric plate is slowly moved into the capacitor until the entire space between the plates is filled. Find the energy U_2 of the dielectric-filled capacitor. The capacitor remains connected to the battery. The dielectric constant is K. Express your answer in terms of A, d, V, K, and ϵ_0.


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