How do you derive Q=CV?

Capacitance, which is C=Q/V, can be derived from Gauss's Law, which describes the electric field between two plates, E=Q/EoA =>E=V=Qd/EoA. From this, capacitance can be written as C=EoA/d.

Capacitance is described as charge storage, which is also C=Q/V, and is illustrated by parallel plate arrangement. From the equation C=Q/V, the units are in coulomb/volt, which is equal to the Farad. Q is the magnitude of charge stored on each plate. V is the voltage applied to the plates. Two parallel plates are the most common capacitor. When the plates are largest and closest together, the greatest capacitance occurs. Capacitance can be increased by inserting a dielectric material between the two plates.