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Obtain the expression for the energy stored per unit volume in a charged capacitor. |
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Answer» Solution :Energy stored PER unit volume is KNOWN as energy density. The energy stored in capacitor, `U=(1)/(2)(Q^(2))/(C)` `=(1)/(2)((sigmaA)^(2))/(1)XX(d)/(in_(0)A)` where Q = `sigmaA` and `C=(in_(0)A)/(d)` `=(sigma^(2)Ad)/(in_(0))` but `(sigma)/(in_(0))=E` `U=(1)/(2) E^(2)in_(0)xxAd` But Ad is the volume of the region between the plates. `:. (U)/(Ad)=(1)/(2) in_(0)E^(2)` is a energy per unit volume . It is denoted by `rho_(E)` or u . `:. ` Energy per unit volume `rho_(E)=(1)/(2) epsilon_(0)E^(2)` |
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