# Difference between the plate of a capacitor and an infinite plane of charges

I would like to understand what is the difference between the plate of a capacitor and an infinite plane sheet of a Charge? I mean, when we use Gauss' law to find the electric field between to plate of a capacitor, we find $$\rho/\epsilon_0$$ (if no dielectric is inserted), with $$\rho$$ the surface charge density of the plate, and we find $$\rho/2\epsilon_0$$ for a infinite plane of a surface charge density $$\rho$$.

• You are approximating the two plates as two infinite planes, and because there are two planes the factor is 1 instead of 1/2
– user65081
Commented Jan 8, 2020 at 15:53

If we consider the field from an infinite plane with charge density $$\sigma$$ then as you say we get a field looking like this:
Now suppose we put a second infinite plate (shown in red) with a charge density $$-\sigma$$ below the first one:
And we end up with a field $$E = \sigma/\epsilon$$ in between the plates and no field outside.