While studying the Capacitors, I read and understood that the Energy stored in a Capacitor which is given by (1/2)Q V.
The next topic was the Energy density and the book stated that the energy stored in a Capacitor is electrostatic potential energy.
When we pull the plates of a capacitor apart, we have to do work against the electrostatic attraction between the plates.
In which region of space is energy stored?
When we increase the separation between plates from $r_1$ to $r_2$ an amount $$Q^2/2 \epsilon_0 A (r_2-r_1)$$ of work is performed by us and this much energy goes into the capictor.In the other hand,new electric field is created in volume $A(r_2-r_1)$. We conclude that the energy is stored in this volume. This last part made no sense to me,the energy supplied is to do the work and the energy goes into the capacitor.
Much like the gravitational pull of the the earth attracts a particle if we increase its height by $h$ (potential increases) and the energy is stored in the body.
Similarly in this case,the energy should be stored inside the capacitor.
Can someone explain what is happening here and why is this not the same as in the case of Earth's gravitation?
Even when there are two small equal and opposite charges, when one charge is pushed away from the other, the potential of the charge increases and it is stored in the charge not in space. Someone explain?