Electric capacitance energy of an electric field

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  • Capacitance of a parallel-plate capacitor:$$C=\varepsilon {\varepsilon}_0 \frac{S}{d}$$
  • Interaction energy of a system of point charges:$$W=\frac{1}{2}\sum q_i \phi_{i}. $$
  • Total electric energy of a system with continuous charge distribution:$$W=\frac{1}{2}\int \phi \rho \,dV.  $$
  • Total electric energy of two charged bodies 1 and 2:$$W=W_1+ W_2 + W_{12},$$where ${W_1}$ and $W_2$ are the self-energies of the bodies, and $W_{12}$ is the interaction energy.
  • Energy of a charged capacitor:$$W=\frac{qV}{2}=\frac{q^2}{2C}=\frac{CV^2}{2}$$
  • Volume density of electric field energy:$$w=\frac{ED}{2}=\frac{\varepsilon {\varepsilon}_0 E^2}{2}$$

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