Q:

How does an inductor store magnetic energy?

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. 

A:

The energy is stored in the magnetic field. I usually think of it as "magnetic field lines repel" but that is not very precise (useful for intuition though).
But along the same lines as your capacitor example (moving the plates to infinity takes work), if you look at a simple current loop there is a force on the wires from the magnetic field generated. This force is repulsive: the loop would like to get bigger. If you could slowly "grow" the loop, you could do work in this way. And the amount of work done is once again equal to the energy stored. Just like for capacitors.
I deliberately stayed away from equations - hoping this verbal picture helps your understanding.

