  Faraday rotation of the polarization plane in magnetized thermal plasma
provides one of the most efficient methods to deduce regular magnetic fields
from radio astronomical observations. Since the Faraday rotation measure RM is
proportional to an integral, along the line of sight, of magnetic field
weighted with thermal electron density, RM is believed to yield the regular
magnetic field averaged over large volume. Here we show that this is not the
case in a turbulent medium where fluctuations in magnetic field and electron
density are not statistically independent, and so contribute to RM. For
example, in the case of pressure equilibrium, magnetic field can be
anticorrelated with plasma density to produce a negative contribution. As a
result, the strength of the regular magnetic field obtained from RM can be
underestimated if the fluctuations in electron density and magnetic field are
neglected. The anticorrelation also reduces the standard deviation of RM. We
further discuss the effect of the positive correlations where the standard
treatment of RM leads to an overestimated magnetic field. Because of the
anisotropy of the turbulent magnetic field, the regular magnetic fields
strength, obtained from synchrotron emission using standard formulae, can be
overestimated. A positive correlation between cosmic-ray number density and
magnetic field leads to an overestimate of the strengths of the regular and
total fields. These effects can explain the difference between the strengths of
the regular Galactic magnetic field as indicated by RM and synchrotron
emissivity data and reconcile the magnetic field strength in the Solar vicinity
with typical strength of regular magnetic fields in external galaxies.
