Cody,
The details of how a target responds to a dynamic magnetic field are complex and probably not of much interest to very many people.
ABOUT CONDUCTIVITY
Materials fall into generally three categories:
#1 Conductors are generally metals that have good conductivity from an overall standpoint. But, even in the conductor category there are significant difference such as good, better and best.
#2 Semiconductors are the materials from which transistors, diodes and etc. are made. These are not good conductors, but they adequate for some very important applications in electronics and are indispensible in today's world.
#3 Insulators are very very poor conductors and are intended to prevent conduction of electrical current
ABOUT LOOPS (e.g. CHAINS)
The eddy currents flow essentially around the outside perimeter of the target to prevent a changing magnetic field from penetrating the target. As a result the magnetic field is diverted around the target. The bigger the loop, the greater distortion of the magnetic field. This is a complex mechanism but follows very well and understandable laws of physics that I can discuss via email with anyone that may be interested.
A small loop creates only a slight distortion of the magnetic field. A large loop creates a larger distortion of the magnetic field. Now a chain is made up of a series of very small loops (of very small diameter) combined to make the large loop ( but of small diameter conductors). The problem is that every small loop must be making intimate contact to the adjoining loop or (from an electrical standpoint) we simply see a lot of small loops and no large loop. A group of small loops just do not create much distortion in the magnetic field and are difficult to detect.
YOUR RING WITH A CUT IN THE BAND
This behaves just as the discription of the chain. In this case there is no intimate contact around the large loop. Even when you touch the ends together, the contact is not intimate. If you soldered the end pieces together (to make intimate contact), then it will behave like a ring again. Even with a sterling silver ring (with the band broken) you will experience the same thing.
Sorry that this is so boring, especially if you do not have a love for physics.
HH,
Glenn