From my little understanding of magnetism and the magnetization process, in order to magnetize a magnet it is better to have a closed magnetic circuit. But how does an air gap affects the magnetization "strength"? Example: Assume that we have a unmagnetized horsehoe magnet with a coil around it for the whole length with a constant current flowing and constrant "coil/length ratio". Will the magnet get more magnetized if we add a keeper to connect the poles? And another example, this time with a small coil (same ampere-turn) in the center of the magnet, how will the keeper affect the magnetization process? And how will this compare to the previous example? I know the question probably requires a better understanding of magnetism in general but I would be glad to find someone able to explain it to me.