Why do we need wires to discharge a capacitor? I've been studying Capacitance and Dielectrics and I can't understand why the capacitor will only discharge if there is a wire connecting them. I understand that when the capacitor is charged up, there is an electric potential difference between the plates that makes the electrons "want to move" from the higher to the lower potential. But since the plates have opposite charges and charges are at the surface of the conductors, why can't the charges move from the positive plate to the negative plate due to Coulomb force?
Apologize me if this is a basic question, but I've been looking for this answer and I just can't find anything of the like, must be because it is really basic.
 A: The Coulomb force is a force trying to move electrons from one plate to the other. That is correct. But remember that there are more forces working here. 
There is a huge resistance against charge motion in an insulator. The resistance pushes back and prevents electrons from just moving into thin air. 
In other and more accurate words: that resistance prevents electrons in the air molecules from moving freely. Only then would air be conducting. Electrons move freely in a metal for example but are bound much tighter in an insulator. So it is not possible to make the "chain reaction" of electron motion happen; it is not possible for an electron on the plate to pass on its "motion" to the neighbor electron in the air molecule, which would then pass it on and on and on all the way to the other side. 
If you wish to make the electrons in the insulating air move (become excited) despite the resistance, you either have to


*

*add enough energy to the air in between for example by making the potential difference so enormously high that electrons can rip themselves loose from the air molecules and move freely (ionizing the air), which is what lightning is all about, or

*connect an easier path between the plates. For example by a metal wire, through which this "chain reaction" of electron motion can happen easily. 
What you are asking is pretty much the basic reason for conductivity in some materials and insulation in others. This is all about the band gap, which electrons have to jump over in order to be free to conduct. And by jumping over, I mean that they have to jump to a higher energy level - they don't physically jump, they just rip themselves loose at the spot they are at. There is no band gap in conductors, but a large one in insulators. And a smaller one in the so-called semiconductors. The above explanation is a try to make that a bit intuitive. I hope it helps you on. 
A: Think about it using Ohms Law. You got a layer of air (or any dielectric) between the plates. It happens that the difference of potential is not big enough to make the electrons move in the air (the air is not a very good conductor). Some capacitors have dielectrics because their operation happens in bigger potential differences (the dielectric will be a even worst conductor than the air). 
A: The Coulomb force is there but in the ideal situation the air and the dielectric contain no free /mobile charge carries, that are insulators, so there is no mechanism for a current to flow between the two metal plates.
In the real world because the air and the dielectric are not perfect insulator the capacitor will discharge.
