[YMP/EM-03009] Electrostatic Energy of a Parallel Plate Condenser

Using the expression for energy density we can compute the energy stored in a charged capacitor. The electrostatic energy is given by the energy per unit volume, ,multiplied by the volume enclosed between {\it i.e.} \( \frac{\epsilon_0}{2}|\vec{E}|^2\) the plates.  Thus we get
\begin{eqnarray}
W&=&\frac{\epsilon_0}{2}(Ad)(\frac{V_0}{d})^2\\ \label{eq19}
\nonumber&=&\frac{\epsilon_0A}{2d}(V_0)^2 \\
&=&\frac{Q^2}{2C}  \label{eq20},
\end{eqnarray}
where C is the capacitance of the parallel plate condenser. \begin{eqnarray} C&=&\frac{\epsilon_0A}{d} \label{eq21}.
\end{eqnarray}