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I know that the maximum energy that can be stored in a capacitor is:

$$ U = \frac{Q^2}{2\,C}\,. $$

What I am asked is to say how much energy was stored when half of the electric charge that could be contained was deposited in the capacitor. I would naturally answer "a quarter", since energy depends on the square of the charge, but the correct answer should be "a half". Because? What am I doing wrong?

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  • $\begingroup$ Where are you finding that the answer should be 1/2? Can you provide a source? $\endgroup$ May 8, 2022 at 20:11
  • $\begingroup$ This is a multiple choice question in Google Classroom. I think at this point it is the professor's mistake. $\endgroup$
    – Monster
    May 8, 2022 at 20:36

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The correct answer would be a quarter. It is very much like the energy stored in a spring is

$$E = \frac{kx^2}{2}$$

Electrons repel each other. If you add electrons to a metal, the metal is charged. The electrons spread out, keeping as far away from each other as possible. It is a lot like little springs pushed them apart.

You can push another electron onto the metal, but it takes a force to do it.

The electrons get crowded a little closer together because there are more of them. The force between each one goes up.

If you push more electrons on, each one requires a little bigger force than the last.

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