Say I have a parallel plate capacitor that has a vacuum between the plates and has electric energy U. If I then add in a dielectric between the plates while the capacitor is charged, the electric energy increases since the dielectric constant increases.
But where does the additional energy come from? Doesn't that violate conservation of energy? I understand that the energy is increased because the permittivity of the dielectric increases, but doesn't it still violate conservation of energy?
Best Answer
We're assuming the charge \$Q\$ is constant (the capacitor is not connected to anything).
The energy is less with the dielectric inserted, by a factor of 1/\$\epsilon_R\$, since \$U = \$ \$Q^2 \over {2\cdot C}\$ and \$ C = \$ \$ C_0 \cdot \epsilon_R\$
It does not go into dielectric absorption, the energy decreases even with a perfect dielectric.
You can extract mechanical energy from the dielectric insertion operation (it's pulled into the gap), and that is where the energy goes.