I am currently reading a chapter in a physics book covering the electric energy stored in a parallel plate capacitor. The author derives the formula for the energy density: $u = 1/2 \epsilon E^2 $ and claims that it applies for any electric field.
Now, this seems to me kind of wrong. Imagining that I would place an electron in empty space, I wouldn't do any work to move it there(because there are no other charges that my electron would interact with). However, the electron would generate a field and thus have energy density associated with it. What am I missing?
