There has been a considerable degree of speculation over the years, that the energy stored in a magnetic field is kinetic energy with a rotational aspect, whereas on the other hand, the energy stored in a capacitor shows all the hallmarks of being potential energy of a similar nature to the energy stored in a mechanical spring. For full details, see this web link, http://www.wbabin.net/science/tombe3.pdf
Most physics teachers are familiar with the analogies that exist between the three important components of an electric circuit, on the one hand, and certain aspects of mechanical and aeronautical engineering on the other hand.
The electrical inductor corresponds to mechanical flywheels, the electrical capacitor corresponds to the mechanical spring, and electrical resistance corresponds to air resistance. As such, the mathematical treatment of any of these analogous pairs is identical, and it is simply a case of substituting the corresponding quantities.
Inductance L corresponds to inertial mass m, and perhaps more accurately to moment of inertia I. Electrical current I corresponds to velocity v, capacitance C corresponds to the reciprocal of the spring constant 1/k, and electrical displacement x corresponds to mechanical displacement x. However, we are about to discuss the fact that electrical displacement is erroneously treated in mathematical calculations as being electrical charge Q.
What makes the capacitor circuit fundamentally different from the inductor circuit is the fact that in the capacitor circuit, the electric current does not have freedom of passage, and it grinds to a halt in a static potential energy state, whereas in the inductor circuit, the electric current has total freedom of passage, and hence on reaching equilibrium, it will continue to flow in a steady state, surrounded by a static magnetic field.
We aim now to try and establish what is the common origin behind both these mechanisms for storing electrical energy. We find that the common origin is an electric sea of rotating electron-positron dipoles, and that in the dynamic state, the two separate theories of linear polarization and rotational magnetization blend together into one unified theory, governed by two laws of electromagnetic induction, which themselves can be combined to derive the electromagnetic wave equation.
It further follows that all matters to do with current in a capacitor circuit, refer only to displacement current, and that we are forced to abandon the traditional notion that electric charge builds up inside the plates of a capacitor.