I think the energy is stored in the field. As an example, if you power up an electromagnet by switching it on and then using a potentiometer to increase the flow of electricity. When you abruptly switch it off you'll get a spark across the switch (could be really big depending on the strength of the field).
The interpretation was that the electron flow created the field and when you stop the flow then the field collapses inducing a new electron flow that jumps the gap of the open switch.