## Capacitance of a parallel plate capacitor

- A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.

- Suppose two plates of the capacitor have equal and opposite charge Q on them. If A is the area of each plate then surface charge density on each plate is
- Suppose two plates of the capacitor have equal and opposite charge Q on them. If A is the area of each plate then surface charge density on each plate is

- We have already calculated field between two oppositely charged plates using Gauss’s law which is and in this result effects near the edges of the plates have been neglected

- Since electric field between the plates is uniform the potential difference between the plates is

where d is the separation between the plates.

- Thus, capacitance of parallel plate capacitor in vacuum is

- We see that quantity on which capacitance of parallel plate capacitor depends i.e.,ε
_{0}, A and d are all constants for a capacitor. - Thus we see that in this case capacitance is independent of charge on the capacitor but depends on the area of its plates and separation distance between the plates.