  With the development of new instrumentation providing measurements of solar
photospheric vector magnetic fields, we need to develop our understanding of
the effects of current density on coronal magnetic field configurations. The
object is to understand the diverse and complex nature of coronal magnetic
fields in active regions using a nonlinear force-free model. From the observed
photospheric magnetic field we derive the photospheric current density for two
active regions: one is a decaying active region with strong currents (AR8151),
and the other is a newly emerged active region with weak currents (AR8210). We
compare the three-dimensional structure of the magnetic fields for both active
region when they are assumed to be either potential or nonlinear force-free.
The latter is computed using a Grad-Rubin vector-potential-like numerical
scheme. A quantitative comparison is performed in terms of the geometry, the
connectivity of field lines, the magnetic energy and the magnetic helicity
content. For the old decaying active region the connectivity and geometry of
the nonlinear force-free model include strong twist and strong shear and are
very different from the potential model. The twisted flux bundles store
magnetic energy and magnetic helicity high in the corona (about 50 Mm). The
newly emerged active region has a complex topology and the departure from a
potential field is small, but the excess magnetic energy is stored in the low
corona and is enough to trigger powerful flares.
