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Obtain the expressionfor capacitance of a parallel plate capacitor without dielectric medium between the plates. |
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Answer» Solution :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 distance between them. The two plates have charges (Q) and -(Q) while the SURFACE charge densities are `(sigma)` and -`(sigma)` respectively.Electric field in the outer region of I and II. `E=sigma/(2epsilon_0)-sigma/(2epsilon_0)=0` In the region between the plates (1) and(2) `E=sigma/(2epsilon_0)+sigma/(2epsilon_0)=sigma/epsilon_0` `E=sigma/epsilon_0=Q/(Aepsilon_0)`...(1) where `sigma=Q/A` As the electric field E is EQUAL to the potentialgradient , for uniform electric field. `E=v/d` v=Ed ....(2) Substituting (2) in equation (1) , `V=Q/(Aepsilon_0)d` The capacitance C of the parallel plate capacitor is `C=Q/V=Q/(Q//Aepsilon_0xxd)=Q/Qxx(Aepsilon_0)/d` `C=(Aepsilon_0)/d` 
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