Capacitance Of Parallel Plate Capacitor

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Capacitance of a Parallel plate capacitor


The parallel plate capacitor consists of two parallel metal plates each of area A and separated by a distance d. The medium between the plates is air. A charge + q are given to the plate P. It induces a charge – q on the upper surface of the earthed plate Q. d is kept small compared with the plate dimensions to enable us to ignore the fringing effects near the ends. Thus electric lines of force starting from plate P and ending at the plate Q are parallel to each other and perpendicular to the plates.

By the application of Gauss’s law,
    electric field at a point} = E = σ
    between the two plates}        ε0

Here, σ = surface density of charge = q/A.

Potential difference between the plates P and Q is
V = ∫0 – E dr = ∫0 – σ dr = σd
        ___________ε0         ε0

The capacitance of the parallel plate capacitor is
    C = q = __σA__ = ε0A
           V    (σd/ ε0)        d
    C = ε0A
            d




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