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I am studying about inductors and capacitors. They store their energy in the form of electric field and magnetic field.Energy is required to create fields.But if we take an isolated charge and nothing else,electric field lines will be created .Does that take energy? I guess not .Then why does energy is stored when electric field lines are formed between the plates of the capacitor?

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  • $\begingroup$ Fields have real existence and not field lines. $\endgroup$ – user36790 Jun 19 '16 at 14:11
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An isolated charge (like, an electron) is produced by ionizing an atom, using energy to pull a single electron free of the atom and pulling that charge far from the opposite-charge ion. So, it DOES take energy to isolate the charge. The isolated charge has an E field around it, but the original uncharged atom had none.

Similarly, when you apply a battery to two plates of a capacitor, there is battery power required to put charge onto the plates, creating the field between those plates. Disconnecting the battery may HIDE the energy source, but the field between the plates is evidence that there was energy supplied (and is still available).

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Even electrostatic fields still contain potential energy in them. The issue here is, an electron (for example) cannot interact with itself. This means that its own field cannot give it a potential energy. So yes, in the case of a lone charge completely isolated, it will create an $\vec E$ field which contains potential energy, but it will do no work until another charge is brought into the system.

Capacitors store half the work the battery does to charge it, in an $\vec E$ field. The energy stored in it is $U = \frac{1}{2}QV$. You can find out why it is half here. Basically it has to do with $I^2 R $ losses.

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