Obtain the expression for the energy stored per unit volume in a charged capacitor.

Explanation

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)`