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Electrostatic Potential and Capacitance

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Energy Stored in a Capacitor

Energy stored in the capacitor is localized on the charges or the plates but is distributed in the field. Since in case of a parallel plate capacitor, the electric field is only between the plates i.e. in a volume ( AXd), the energy density

straight rho subscript straight E space equals space straight U subscript straight E over volume space equals fraction numerator begin display style 1 half end style CV squared over denominator straight A space straight x space straight d end fraction space equals 1 half open square brackets fraction numerator straight epsilon subscript 0 space straight A over denominator straight d end fraction close square brackets straight V squared over Ad
straight rho subscript straight E space equals 1 half straight epsilon subscript 0 open parentheses straight V over straight d close parentheses squared space
as space straight E space equals straight V over straight d
straight rho subscript straight E space equals space 1 half straight epsilon subscript 0 straight E squared

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