A new method is suggested for determinating magnetic fields of astrophysical objects, based on the allowance for the effect of Faraday rotation of the polarization plane in the process of radiation scattering by electrons. Problems of multiple scattering in magnetized accretion disks and single scattering in a magnetized corona and a wind around the accretion disk are solved. Calculated values of polarization parameters are compared with the results of spectropolarimetric observations of quasars and active galactic nuclei. It is shown that the standard theoretical model of an accretion disk with electron scattering without magnetic field does not well agree with the observations. The inverse problem is solved: the radial dependence of the magnetic field in the accretion disk is determined from the dependence of the polarization degree on wavelength. It is shown that different models of a magnetized accretion disk with equipartition between the magnetic and thermal energies give different dependence of polarization on wavelength. Magnetic fields near the central engine are determined for galaxies MCG-6-30-15, Mrk 6, NCG 4154, 3516, 5548, and for microquasar SS 433.

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