## 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.,ε0 , 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.