Understanding Capacitors [duplicate]

I cannot understand how capacitors work.

1. Electric field is supposedly uniform between the parallel plates of a capacitor. But how? Since $E=\frac{kq}{d^2}$, shouldn't the electric field approach infinity as one approaches either of the two plates ($d=0$), while it would be smaller in the middle?

2. There is air between the capacitors, right? Air isn't a conductor, is it? Circuits in which the wires are interrupted by air aren't closed, are they? Yet circuits still function with capacitors in them and charge is brought from one plate to the other while there is air between the plates. What is going on there?

Thank you

marked as duplicate by Alfred Centauri, user36790, CuriousOne, John Rennie, AccidentalFourierTransformMay 2 '16 at 9:25

• – user83548 May 1 '16 at 21:58
• 2. circuits function because charge accumulates in the plates, it does not jump across the plates – user83548 May 1 '16 at 22:00

$$\nabla\cdot{}E=\frac{\rho}{\varepsilon_0}$$