Question

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

Answer 1

Let in a parallel plate capacitor the plates are 'd' apart, and its charged by Q

Area of plates = A

Volume of capacitor = Ad

charge per unit area,

So, energy stored in it, $\sigma =\frac{Q}{A}$

$E=\frac{Q^2}{2C}$

also, capacitance is given by : $C=\frac{A{ϵ}_o}{\alpha }$

So energy per unit volume,

$\frac{E}{V}=\frac{Q^2}{2CV}=\frac{Q^2\times d}{2times{ϵ}_0\times Ad}=\frac{Q^2}{2{ϵ}_0{A}^2}=\frac{{\sigma }^2}{2t_0}$