I am trying to figure out what the potential energy of an inductor with a current really means. In a capacitor, the energy stored works like this: if you let the plates attract each other, before colliding the plates would have total kinetic energy equal to that potential we gave it before. We can derive the equation $\frac {1}{2} C V^2$ by expressing $dW$ in terms of $V$ and $dQ$, then doing some integrating. This makes sense because the electric field is conservative and so we can integrate it to find a voltage.
However, I don't really understand the energy of inductors. The magnetic field doesn't even have a potential associated with it!
Of course there are some other questions on this topic, and so I think I should give some explanations as to why these didn't answer my question:
This answer : I understand how an inductor can produce a voltage by a changing magnetic field which produces an electric field, but what about an Battery-RL circuit going on for a long time? The voltage across the inductor pretty much depletes to zero exponentially, but there is still a current, therefore a magnetic field, therefore magnetic energy!
This question dodges the question completely and the link doesn't work for me.
I know this is a really old question that you guys are probably sick of seeing but it would be very helpful for me to understand where this energy arises from.