  In high-quality solid-state systems at low temperatures, the hydrodynamic or
the ballistic regimes of heat and charge transport are realized in the electron
and the phonon systems. In these regimes, the thermal and the electric
conductance of the sample can reach abnormally large magnitudes. In this paper,
we study the Hall effect in a system of interacting two-dimensional charged
particles in a ballistic regime. We demonstrated that the Hall electric field
is caused by a change in the densities of particles due to the effect of
external fields on their free motions between the sample edges. In
one-component (electron or hole) systems the Hall coefficient turns out to one
half compared with the one in conventional disordered Ohmic samples. This
result is consistent with the recent experiment on measuring of the Hall
resistance in ultra-high-mobility GaAs quantum wells. In two-component
electron-hole systems the Hall electric field depends linearly on the
difference between the concentrations of electrons and holes near the charge
neutrality point (the equilibrium electron and hole densities coincide) and
saturates to the Hall field of a one-component system far from the charge
neutrality point. We also studied the corrections to magnetoresistance and the
Hall electric field due to inter-particle scattering being a precursor of
forming a viscous flow. For the samples shorter than the inter-particle
scattering length, the obtained corrections govern the dependencies of
magnetoresistance and the Hall field on temperature.
