Derive the expression Parallellplates capacitance with air
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The most common capacitor consists of two parallel plates. First, we derive the capacitance which depends on the area of the plates A and their separation d. According to
Gauss's law, the electric field between two plates is:

Since the capacitance is defined by

one can see that capacitance is:

Thus you get the most capacitance when the plates are large and close together.
If a dielectric material is inserted between the plates, the microscopic dipole moments of the material will shield the charges on the plates and alter the relation. Materials have a
permeability e which is sometimes given by the relative permeability k, e = ke0. The capacitance is then given by:

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