Steps to calculating capacitance
1. Imagine the capacitors are charged to +Q and -Q
2. Use Gauss' Law to find the electric field between them
So we know from the derrivation in the previous post that the electric field between two parallel plates with +Q and -Q (or and ) is:
Because we did the derrivation for the this in the previous post we can skip steps 1 and part of step 2.
(since l is just the distance d between the plates)
(from step 2.5)
(from step 3)