Enhanced capacitance by magnetism?

Question

Consider the first picture. This is much like a parallel plate capacitor charged by a battery. But instead of parallel plates we are using parallel rings. The rings are attracting each other because of the electrostatic force created by the static charges in them. When the electrostatic potential equals to the voltage V provided by the battery no more charges can be charged in the capacitor, right?

Now consider the second picture.

We open each ring and insert a batteries in their loops. So there are I and -I currents flowing in each ring, as it is shown in the picture. The currents in each ring goes in opposite direction with respect to the other. The opposite currents create repulsive force between them. It is safe to say that, because of the magnetic force due to the currents, electrons of each ring repeal each other. Yet on the other hand we have electrostatic attractive forces between the rings. Because there are missing electrons in one ring and surplus electrons in the other. As the attractive forces are being partially screened by repulsive forces due to the currents, would it be correct to assume that with the same V voltage of the charging battery more charge can be charged in the capacitor, thus the capacitance is enhanced due to the currents in the rings?

P.S.: This is not a homework question, so please don't tag it as so. I hope that my English is not that terrific to get confused on that.

Answer 1

Capacitance is not about forces between armatures, it's rather the relation between the voltage and the current. Your set up only adds a mutual inductance. This alleviates the attractive electric stress on the armature by adding opposing magnetic stress. However, the capacitance of the system does not change.

For your comment, you are assuming that the magnetic force on the ring is the same as the one of a free charge going from one armature to the other. This is not the case, the test charge only sees the magnetic field created by the two rings which will not induce a particular force towards one or the other. In fact, the magnetic force does not work, so there is no extra energy barrier to overcome which is what capacitance measures. The only effect is to distort the trajectories and make them helicoidal.

More generally, I think that you are confusing capacitance with breakdown voltage. For electrical breakdown, after a quick research, magnetic fields seem to decrease the breakdown voltage (not an expert though). However, since the magnitude of the field is relevant, it would be best for your setup for the two currents to circulate in the same direction, rather than opposing ones. As you presented, the magnetic field even cancels around the center, decreasing the effect of lowering the breakdown voltage.

Hope this helps.