Hi,
You should probably start from the basics. What that means is abandon the core constructions and turn to the single, straight wire where the operation becomes more apparent. Magnetic cores just complicate the issue. This is the way to start to learn any new theory. Start with the basics, then add complications later.
With a single straight wire we have lines of flux encircling the wire. The circles would be symmetrical about the wire. From the time the first electron starts to move in the wire in classical theory the field emanates out to infinity, so the flux lines go out to infinity even though there is very little current right away. That means we have flux circles that are 1000's of meters in diameter, and some that are only nanometers in diameter. That means some circle are inside the wire and some circles are outside the wire.
When we increase the current level, the density of these flux lines increases. That would be equivalent to generating more circles, and so we see a denser packing in the space around the wire. We can visualize this by thinking of circles that start at the center of the wire and get larger and larger. Although that's not yet the enire picture, it will suffice for now. So the circles get larger and larger but there are more smaller circles to take their place, and all having origin at the wire.
So what happens when we decrease the current. When the current decreases, the circles start to collapse back onto the wire, and each line is said to 'cut' the wire in the way a knife might cut a loaf of bread. When a cricle gets small enough to match the diameter of the wire, it soon start to become smaller then the wire, and so it now resides again inside the wire, and that is considered "cutting' the wire. That is the point at which the back emf from that flux circle is generated.
To get a slightly more clear picture of what is happening here we have to turn to the idea of a multi filament wire. That is a wire that is made up of a larger number of tiny filaments that run perfectly parallel to each other. Their total cross section matches the cross section of the original wire. This can be thought of as a simple multi strand wire, where each strand is in parallel to each other with no twisting.
Now when the first circle falls back onto the wire, it first cuts the outer strands, and so only they generate a back emf. When they get even smaller then they cut the next smaller diameter of strands, and generate more back emf. This happens until they get back to a diameter of zero.
There are some circles that are already inside the wire diameter, so they start generating back emf right away in the same manner.
In this classical theory once current is applied to the wire the flux circles, with no other influence, would reach a diameter of infinity in zero time, but in real life it would take about 8 minutes for a flux ring to reach the Sun in our solar system. Since the field drops off so fast though as we get farther and farther away from the wire, it sometimes doesnt matter that much.
The reaction of the current to the collapsing flux lines is known as "self inductance". It is equivalent to the number of flux lines that fall back onto the wire when the current is reduced to zero from a level of unity. Thus the self inductance is obtained by integrating all the flux lines from the axial center of the wire to infinity (and times a constant)