In the above problem, it states that the dielectric fluid is "pulled up" by an electric force. However, I don't see why this should be true. The electric field (and therefore any electric force) between the plates of the capacitor is horizontal, so there should be no vertically acting force pulling the fluid up. What is wrong with my reasoning, and how does one go about solving the problem?
Also, what does it mean by the work done by the battery? Is it simply $C(x)\cdot V^2_0$?
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