Energy stored in capacitor derivation (why it's not QV) | Electrostatic potential | Khan Academy

To calculate the energy stored in a capacitor, we calculate the work done in separating the charges. As we separate more charges, it takes more work to separate even more, due to increased repulsion. Hence, to find the total work done, one needs to integrate. Let's see how we can set up this integral and find the total work done.

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Created by Mahesh Shenoy

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[not_enough_data_]

For hopefully a bit more intuition on why it's 1/2:

In the naive case, let the x-axis be the charge moved so far, and then draw a graph of y = voltage (ie a constant here). Then to compute the work done, you can take an integral of voltage dq, or in other words the area under this graph from x=0 to x=Q. For this naive case, that's just the area of a rectangle = base x height = charge x voltage

In the more sophisticated case, you know that the voltage isnt constant, and instead it's proportional to the charge moved so far. That means the graph will slope upwards away from the origin, cutting the rectangle you had before in half. Your total work done is still the same integral, so it's still the area under the graph, which in this case is the area of a triangle = 1/2 base x height = 1/2 charge x final-voltage

If you see a factor of 1/2 anywhere else, for example in kinetic energy, you can often interpret it in a similar way

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[jacobvandijk]

THE USUAL ERROR: There is no energy in this field. The potential energy is only with the displaced electrons!!! The battery did work on THEM, not on some field that wasn't even there in the first place. Think of this: If you roll a ball upon a hill, then the ball acquires potential energy, not the gravitational field.

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[marvelcalculus]

You can take the battery is doing work to move the charged particle e^- by spending energy which is stored as chemical energy in it and by this you can neglect the attraction since electrolyte is present in battery does not create attraction to e^- and so it is applicable in reality

[straightforward]

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[moratasa]

can you please do more on capacitor and ac circuits

[rutusodha-csmt]

please explain method of images topic too.