Parallel Plate Capacitors
The defining equation of capacitance isor Capacitance = Charge per unit Voltage. Capacitance is constant within certain limits, and is a feature of the construction of the capacitor.
The simplest capacitor is the parallel plate capacitor, which consists of two conducting plates connected to a potential difference.
If the charge density on each plate isthen
Apply Gauss's Divergence theorem to each plate:
since the fieldexists only between the plates and is uniform there, and the total charge enclosed by the volume of the plate isThis equation simplifies toand sincewe havehence
gives the capacitance of a parallel plate capacitor.