Do Maxwell's equations conserve energy? [closed]

I was wondering if Maxwell equations conserved energy. Jackson is not really convincing about the whole Poynting theorem (neither currently google found articles which just assume a bunch of stuff).

Does anyone have an insightful/intuitive explanation or should I just take it for granted?

Rotational field means the curl is different than $0$.
Conservative force needs $\nabla$x$\vec{F} = 0$
Is energy conserved?

• What's not convincing about the Poynting theorem? – Phoenix87 Nov 8 '17 at 22:52
• For a system of electrically charged matter in flat spacetime, the SET is conserved (i.e. $\partial_\mu \left(\Theta^{\mu\nu} (F) + T^{\mu\nu}_{\text{matter}}\right) = 0$, with $\Theta$ the symmetric Belinfante-Rosenfeld tensor). Perhaps you can read the book by Barut on electrodynamics (Barut, A. - Electrodynamics and classical theory of fields and particles) for an alternate proof. – DanielC Nov 8 '17 at 23:32
• You don't need any assumptions beyond Maxwell's equations and the Lorentz force law. Perhaps you could elaborate on what you find unsatisfactory. – J. Murray Nov 9 '17 at 2:00
• I'm downvoting this question until clarification comes. It's really annoying when someone states that some derivation is not convincing and doesn't point out any problems. What do you expect to get as an answer? – OON Nov 9 '17 at 10:02
• I expected to get an answer considering why rotating fields in ME are considered conservative. A physical answer, rather than a mathematical derivation. – Dominik Car Nov 9 '17 at 21:49

• This is what I mean. You have a circular field, the rotation of the field is $!=$ $0$. If the rotation of the field is $!=$ $0$, the energy is not conserved. – Dominik Car Nov 9 '17 at 17:06