The equation for the energy density in a region of space where there is electric field, $\epsilon_0E^2/2$ implies that energy in the electric field can only be positive. Consider, however, the energy of interaction between two oppositely charged objects, which is negative $-\frac{kQ_1Q_2}{r}$. Is it because we only consider the negative part when performing calculations, while the entire energy is actually positive, since we can always add an arbitrary constant to the value of the energy and make it so that it is technically positive?
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$\begingroup$ It's actually worse than that: the total classically predicted energy in the field of a single point charge is infinite, i.e. classical electromagnetism returns the incorrect answer to the question of the microscopic structure of point charges. This problem can't be resolved at the level of classical physics. It takes quantum field theory to predict correctly what happens "near" a point charge like an electron. Even with quantum field theory there is no obvious way to predict the total background energy of the vacuum correctly at this moment. $\endgroup$– FlatterMannCommented Mar 28, 2023 at 16:48
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$\begingroup$ @RudyJD He is talking about the potential, though, not the force. We do choose the sign of the potential so that the force between two charges is predicted correctly. $\endgroup$– FlatterMannCommented Mar 28, 2023 at 16:50
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$\begingroup$ @FlatterMann Yeah i misread question lol. comment deleted :P $\endgroup$– RudyJDCommented Mar 28, 2023 at 16:52
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$\begingroup$ Could this thread and this document be helpful? $\endgroup$– VangiCommented Mar 28, 2023 at 16:53
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$\begingroup$ Related. You are correct in that in electrostatics, energy is only meaningfully defined up to an additive constant. $\endgroup$– PukCommented Mar 28, 2023 at 17:01
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