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Flux loops and Hall probes are being installed on selected segments of the steel flux return of the 4 T solenoid of the compact muon solenoid (CMS) detector under construction at CERN (European Center for Nuclear Research). This steel also serves as part of the muon detection system of CMS and accurate characterization of the magnetic flux density in the steel as elsewhere in the detector is required. Voltages induced in the flux loops during fast discharge of the solenoid will be sampled and integrated to measure the change in average flux density in the steel during the discharge. Hall probes mounted on the surface of the steel segments will provide information about the fields internal and external to the steel. In the laboratory work reported herein small iron discs with flux loops on their peripheries and Hall probes on their flat surfaces are magnetized between the pole tips of a laboratory standard magnet and controlled power supply. The voltages induced in the flux loops during charging and discharging of the magnet are integrated and compared with the Hall probes which sample the fields immediately external to the discs. The experimental work reported here will provide interpretation of the flux coil and Hall probe measurements from the CMS magnet when it is commissioned in 2005.