  This paper discusses a quasi-static evolution of a force-free magnetic field
under slow sheared footpoint motions on the plasma's boundary, an important
problem with applications to the solar and accretion disk coronae. The main
qualitative features of the evolution (such as field-line expansion and
opening) are considered and a comparison is made between two different
geometrical settings: the Cartesian case with translational symmetry along a
straight line, and the axisymmetric case with axial symmetry around the
rotation axis. The main question addressed in the paper is whether a continuous
sequence of force-free equilibria describes the evolution at arbitrarily large
values of the footpoint displacement or the sequence ends abruptly and the
system exhibits a loss of equilibrium at a finite footpoint displacement. After
a formal description of the problem, a review/discussion of the extensive
previous work on the subject is given. After that, a series of simple
scaling-type arguments, explaining the key essential reason for the main
qualitative difference between the two geometry types, is presented. It is
found that, in the Cartesian case, force-free equilibria exist at arbitrarily
large values of shear and the field approaches the open state only at infinite
shear, whereas in the axisymmetric case the field opens up already at a finite
shear.
