  We explore in this paper the ability to constrain the Galactic magnetic field
intensity and spatial distribution with the incoming data from the Planck
satellite experiment. We perform realistic simulations of the Planck
observations at the polarized frequency bands from 30 to 353 GHz for two
all-sky surveys as expected for the nominal mission. These simulations include
CMB, synchrotron and thermal dust Galactic emissions and instrumental noise.
(Note that systematic effects are not considered in this paper). For the
synchrotron and thermal dust Galactic emissions we use a coherent 3D model of
the Galaxy describing its mater density and the magnetic field direction and
intensity. We first simulate the synchrotron and dust emissions at 408 MHz and
545 GHz, respectively, and then we extrapolate them to the Planck frequency
bands. We perform a likelihood analysis to compare the simulated data to a set
of models obtained by varying the pitch angle of the regular magnetic field
spatial distribution, the relative amplitude of the turbulent magnetic field,
the radial scale of the electron and dust grain distributions, and the
extrapolation spectral indices for the synchrotron and thermal dust emissions.
We are able to set tight constraints on all the parameters considered. We have
also found that the observed spatial variations of the synchrotron and thermal
dust spectral indices should not affect our ability to recover the other
parameters of the model. From this, we conclude that the Planck satellite
experiment can precisely measure the main properties of the Galactic magnetic
field. An accurate reconstruction of the matter distribution would require on
the one hand an improved modelling of the ISM and on the other hand to use
extra data sets like rotation measurements of pulsars.
