An annular magnetic core made of an Fe-based, nano-crystalline, soft-magnetic alloy, in which part of Fe is substituted by Ni and/or Co; having AC specific permeability µr 100k(50) of 4000 or more at a frequency of 100 kHz and DC magnetic field intensity of 50 A/m, AC specific permeability µr 100k(150) of 2500 or more at a frequency of 100 kHz and DC magnetic field intensity of 150 A/m, and the maximum permeability µ Max of 8000 or less, and a magnetic flux density B 400 of 1.3 T or more, at DC magnetic field intensity of 400 A/m.