[LECS/EM-03003]-Electrostatic Energy

The electrostatic  energy of a continuous charge distribution is defined as the energy required to assemble the charges at  infinity into the positions as in the given distribution. For a continuous charge distribution it is shown to be \( \dfrac{\epsilon_0}{2}\iiint(\vec E\cdot\vec E) dV\) . Thus a volume of space having nonvanishing electric field has energy density  \(\dfrac{\epsilon_0}{2}(\vec E\cdot\vec E)\).The expression for the electrostatic energy reduces to the usual answer \(\frac{1}{2}  CV^2\) for a charged parallel plate capacitor. For a  uniformly charged sphere of radius \(R\) the electrostatic energy is proved to be equal to \(\frac{3}{5}\Big(\frac{Q^2}{4\pi\epsilon_0 R^2} \Big)\).