Derive an expression for the capacity of a parallel plat capacitor, When the medium between the plats is partially filled by a dielectric medium
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Solution :
Consider a parallel-plate capacitor, consisting of two parallel plates A and B separated by a distance d as shown in the figure. Let A be the area of each plate and k the dielectric constant of the medium between the plates. Plate B is connected to the Earth. Suppose that the capacitor is charged such that the charges on plates A and B are +Q and -Q, respectively.
If the area A is very large and the distance between the plates is very small, the electric field in the region between the plates is almost uniform except at the edges. The magnitude of the electric field E→ at a point between the plates and the potential difference V between the plates are related by E=V/d.
But, E=σε0k, where ε0 is the permittivity of free space and σ is the surface charge density.
∴σε0k=Vd ...(1)
Since σ=QA,E=Qε0kA=Vd ...(2)
The capacitance of a capacitor is C=QV
∴C=ε0kAd ...(3)
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