A normal quadrupole prototype magnet with 266-mm long, 105-mm aperture has been designed and fabricated by IHEP. Total of 88 quadrupole magnets are under fabrication. The multipole components, magnetic field gradient and transfer function of the quadrupole magnets were measured in September 2004, using an updated measurement system, which includes a rotating coil measurement system and a Hall Probe measurement system. This paper mainly describes the updated harmonic coil magnetic field measurement system and provides the measurement results for BEPC II quadrupole magnets
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