Derive the expression for the capacitance of a parallel plate capacitor having plate area A and plate separation d.
A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.
Let A be the area of each plate and d be the separation between them. The two plates have charges Q and −Q. Plate 1 has surface charge density, σ = Q/A,
And plate 2 has a surface charge density −σ.
Electric field in different regions:
Outer region I:
Outer region II:
In the inner region between plates 1 and 2, the electric fields due to the two charged plates add up.
The direction of electric field is from positive to the negative plate. For uniform electric field, potential difference is simply the electric field times the distance between the plates.
Capacitance (C) of the parallel plate capacitor, `C=Q/V=(epsilon_0A)/d`
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