 Electrostatic energy

Electrostatic energy is energy stored in an electrostatic configuration. For localized charges in vacuum, with suitable decay at infinity, equivalent forms are $U=\frac{1}{2}\int \rho \varphi dV$ and $U=\frac{{ϵ}_0}{2}\int |\mathbf{E}{|}^{2}dV$. The factor of one half avoids counting each pair interaction twice.

An ideal capacitor provides a finite example: charging it from zero gives $U=Q^2/(2C)=C{V}^2/2$. Point-charge self-energies diverge in the elementary continuous-field model, so pair interaction energy must be distinguished from that singular self contribution. Boundaries and an applied voltage source also matter when comparing changes in stored field energy with mechanical work.