Define electric capacity. Derive an expression for the capacitance of a parallel plate capacitor in which a dielectric medium of dielectric constant K fills the space between the plates. Draw the necessary diagram.
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Solution
Capacitance or electric capacity indicates the ability of a system to store charge. It is defined as the ratio of charge stored in the conductors to the potential difference across the conductors. Its SI unit is Farad (F). Hence:
C=QV
To derive the expression of capacitance of parallel plate capacitor of conductor area A and distance between the conductors as d with a dielectric of dielectric constant K carrying a charge Q and potential difference V, refer to the attached figure.
Electric field between plates of the capacitor can be found using Gauss Law.
E=σKεo
E=QKεoA as σ=QA
Electric field is defined as the gradient of potential.