Momentum of capacitor in a uniform magnetic field

We are observing ideal, charged, parallel plate capacitor placed in uniform magnetic field parallel to plates. Whole system is at rest and isolated (we have forces that hold plates separated, but net force is zero) and, according to "Center of energy theorem", it must contains zero total momentum. System has non-zero momentum stored in electromagnetic field so we must have some "hidden" momentum so the total momentum would be zero? Where is it "hiding"?

• Possibly related: physics.stackexchange.com/q/7218 Sep 23 '14 at 2:53
• There is nothing paradoxical about Poynting vector cause divS=0 and energy doesnt flow. Question is more about correct application of "Center of energy theorem". Total momentum should be zero? P.S. I have already seen both of link posted in above two comments and they are not solution of this problem. Thank you anyway! Sep 23 '14 at 9:25
• I wanted to say that conservation of energy is satisfied, not that energy doesnt flow. Sep 23 '14 at 9:53
• @Mihailo_Serbia, the Griffith's paper link seems to directly address your question: "What about a capacitor in the magnetic field of a solenoid? In this case the hidden momentum is located in the solenoid (that is where the moving charges are), and the electric field responsible for the variation in $\gamma$ must be the exterior fringing field of the capacitor." Stating that there is a uniform magnetic field and then not looking for momentum stored in the source of that field may be the problem here. ate.uni-duisburg-essen.de/data/postgraduate_lecture/… Sep 23 '14 at 11:44
• Thank you! Ill study it carefully. At the beginning I refused to pay attention on fringing fields and blindly calculated momentum using Poynting theorem. It is so cool that problem make us to watch source of field. Sep 23 '14 at 11:56