We aim to measure the helicity of the coronal magnetic field of an active region based on the linear force-free field(LFFF) assumption. With a value of the force-free a, the coronal field is constructed from the extrapolation of SOHO/MDI magnetograms, and the constructed field lines are compared with the coronal loops in the EUV images taken by SOHO/EIT. The force-free- field that best fits the loops is used to calculate the helicity of the active region. By applying this method to the solar active region AR 10696 during its first rotation, we have examined the temporal variation of the magnetic helicity, and have compared it with the accumulated amount of the helicity transferred to the corona through the photosphere which was determined independently. Our results are summarized as follows. 1) The magnetic field of the active region is not fully LFF. The force-free a varies from loop to loop, with a deviation of 30 to 45%, which gives us a very conservative estimate of the uncertainty in the coronal helicity determined using the LFF model. 2) The measured value of the coronal magnetic helicity was close to the accumulated amount of injected helicity with a discrepancy of 10 ~ 30%. 3) The coronal magnetic helicity decreased after CMEs occurred, with the amount of decrease being close to what may have been carried away by the CMEs. Our results support that the LFF field extrapolation method can be used to infer the magnetic helicity of an active region within an uncertainty of a few tens of percent.
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