  Our understanding of coronal phenomena, such as coronal plasma
thermodynamics, faces a major handicap caused by missing coronal magnetic field
measurements. Several lines in the UV wavelength range present suitable
sensitivity to determine the coronal magnetic field via the Hanle effect. The
latter is a largely unexplored diagnostic of coronal magnetic fields with a
very high potential. Here we study the magnitude of the Hanle-effect signal to
be expected outside the solar limb due to the Hanle effect in polarized
radiation from the H {\sc{i}} Ly$\alpha$ and $\beta$ lines, which are among the
brightest lines in the off-limb coronal FUV spectrum. For this purpose we use a
magnetic field structure obtained by extrapolating the magnetic field starting
from photospheric magnetograms. The diagnostic potential of these lines for
determining the coronal magnetic field, as well as their limitations are
studied. We show that these lines, in particular H {\sc{i}} Ly$\beta$, are
useful for such measurements.
