| Magnetic field plays central role in solar activity. Almost all kinds of solar activities, such as sunspot, solar flare and coronal mass ejection, are associated with solar magnetic field. The measurement of solar magnetic field and the non-potential characteristic of solar activity are important to explain the physical mechanism and dynamical process of solar activity. In this dissertation the both are studied. The main results are as follows:1. The effect of Faraday rotation on the azimuths of transverse fields observed by the Solar Magnetic Field Telescope at the Huairou Solar Observing Station. It is believed that the Faraday rotation is insignificant in the far wing of the line in the theoretical analysis. We make a comparison between the azimuths of 70 couples of transverse fields observed at line center and in the wing of the working spectral line of the telescope. From the comparison we found that the influence of Faraday rotation is slight for the weak magnetic fields (less than 1000Gauss) and becomes significant for the strong fields (bigger than 1000Gauss). And the influence of Faraday rotation is insignificant when the incline angle γ is less than 30°. It becomes significant when 30 °<γ <60° and becomes slight when the incline angle γ is bigger than 75°. The average influence of Faraday rotation on the measurements of the azimuths of transverse fields observed by the telescope is 13°.2. The effect of Faraday rotation on the helicity computation using observations from the Solar Magnetic Field Telescope at the Huairou Solar Observing Station. The helicities derived from 70 couples of vector magnetograms obtained at the line centerand in the wing of the line were compared. The results show that the influence of Faraday rotation on the helicity computation is insignificant when the strength of magnetic fields is less than 1000 Gauss and becomes significant as the increase in the strength of magnetic fields. The influence is insignificant when the incline angle γ is less than 30° or bigger than 30°. And when 30° <γ<75°, the influence increases with the value of the incline angle.3. The evolution of the magnetic shear angles and the non-potential energies in the ascending phase of solar cycle 23. We selected 700 vector magnetograms of 234 active regions observed from 1995 to 1998 by the Solar Magnetic Field Telescope at the Huairou Solar Observing Station. The flux of longitudinal magnetic fields, the magnetic shear angle and the non-potential energy of these vector magnetograms are calculated. And the evolutions of the monthly mean values of above parameters are derived. The results show that from the minimum of solar cycle 22 to the ascending phase of solar cycle 23, not only the number and area of solar active regions, the flux of longitudinal magnetic fields and the total energy of the active regions are increased, but also the density of non-potential energy of the solar active regions is increased. Although the evolution of magnetic shear angle has not such trend, the sign and value of the magnetic shear angle change slow at the minimum of solar cycle 22 and change rapidly in the ascending phase of solar cycle 23, which show that the non-potentiality becomes more and more complicated as the coming of solar maximum years.4. The statistical distribution of magnetic shear angle in the ascending phase of solar cycle 23. We selected 759 vector magnetograms of 274 active regions observed from 1996 to 2000 by the Solar Magnetic Field Telescope at the Huairou Solar Observing Station and calculated their magnetic shear angles. The histograms of magnetic shear angles of the total active regions, the active regions in the north hemisphere and the active regions in the south hemisphere are derived. The distributions were fitted well by Gaussian curves. And the distribution of the magnetic shear angles exhibits the hemisphere sign rule as the asymmetry of helicity. In our dataset, 53% of the active regions in the south hemisphere have positive shear angle and 62%...
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