We aim to estimate the contribution of the radial component of the Lorentz
force to the gas rotation in several types of galaxies. Using typical
parameters for the exponential scale of synchrotron emission and the scale
length of HI gas, under the assumption of equipartition between the energies of
cosmic rays and total magnetic fields, we derive the Lorentz force and compare
it to the gravitational force in the radial component of the momentum equation.
We distinguish the different contributions between the large-scale and the
small-scale turbulent fields by Reynolds averaging. We compare these findings
with a dynamical dynamo model. We find a possible reduction of circular gas
velocity in the very outer parts and an increase inside a radius of four times
the synchrotron scale length. Sufficiently localized radial reversals of the
magnetic field may cause characteristic modulations in the gas rotation curve
with typical amplitudes of 10-20 km/s. It is unlikely that the magnetic field
contributes to the flat rotation in the outer parts of galaxies. If anything,
it will \emph{impede} the gravitationally supported rotation, demanding for an
even higher halo mass to explain the observed rotation profile. We speculate
that this may have consequences for ram pressure stripping and the truncation
of the stellar disc