If an inductor "stores energy in a magnetic field", what does that mean exactly? It sounds like there's an invisible force field emanating from the coil or orbiting around the wire. As if electrons are jumping through the insulation and just hanging out; suspended there in mid-air. And the circuit can access them whenever the load requires it?
Does that sound about right?
No, here is what's happening.
When a coil of wire is carrying a flow of electric current, it creates a magnetic field that loops through the center of the coil and out & around the exterior of the coil. The field is conveniently represented by field lines that trace out the direction a compass would point at various locations in the field.
To build up a magnetic field like this requires the performance of (electrical) work- the stronger the field, the more work is required. In this sense, the work performed to propagate the field is stored in the field itself. If you then cut off the current that is sustaining the field, the field shrinks back down and pumps its stored energy back into the coil, inducing a current to keep flowing in it after the original current has been switched off.
The mechanical analog of a coil is a mass. If we push on the mass, it resists at first but then begins to move at some velocity v. The work we performed to set the mass in motion is then stored in it as kinetic energy. If we stop pushing, the mass wants to keep moving and to bring it to a halt requires us to extract that kinetic energy.
