Derive an expression for the nergy stored in a capacitor. Find an expression for the energy density in an electric field E free space.

Explanation

(ii) Energy Density of an Electric Field The energy stored per unit volume of a capacitor is called energy density.
The capacitance of parallel plate capacitor in free space is given by `C_(0)=(epsilon_(0)A)/(d)`
The electric firld intensity between the plates will be
`E=(V)/(d)rArrV="Ed"`
So, `W=1/2C_(0)V^(2)=(1)/(2)(epsilon_(0)A)/(d)("Ed")^(2)rArrW=1/2epsilon_(0)E^(2)"Ad"`
Here, Ad = volume of the space between the plates = v
`W=1/2epsilon_(0)E^(2)v`
So, density of an electric field will be
`U=(W)/(v)=1/2epsilon_(0)E^(2)`
If the electric field is established in a dielectric medium of permittivity `epsilon`, then
`U=1/2epsilonE^(2)rArrU=1/2Kepsilon_(0)E^(2)" "[becauseepsilon=epsilon_(0)K]`
where, K = dielectric constant.