A capacitor can be considered a kind of battery. It has a charged and a discharged state, just like a chemical or atomic battery would. In every important respect, this does not change the identity of the scenario. I'm now going to stipulate that whatever it is you have in mind, it has nothing whatsoever to do with the Earth's or any other external magnetic field. This would violate the isolation of the system, for one thing. There is something satisfying about the kind of mathematical rigor it takes to publish over 100 pages of math to derive the identity of unity, 1 = 1. Likewise, I find it satisfying that this problem has already beaten the whole issue of COM to a pulp, and in the process seems to have proven a number of theorems that would seem to be a precursor to understanding all of the concepts used in Newton's laws; that mass / inertia exists, that it is possible for it to move, thereby moving its center of mass, and that energy density can be increased or decreased at will to support moving the COM. Not to mention the intimate relationship between linear and angular (spin) momentum. COM ideas were used to derive E=mc^2. It isn't like it is a trivial matter to consider in detail. Before 1905, no one knew that.