  Force-free extrapolations are widely used to study the magnetic field in the
solar corona based on surface measurements. The extrapolations assume that the
ratio of internal energy of the plasma to magnetic energy, the plasma-beta is
negligible. Despite the widespread use of this assumption observations, models,
and theoretical considerations show that beta is of the order of a few percent
to more than 10%, and thus not small. We investigate what consequences this has
for the reliability of extrapolation results. We use basic concepts starting
with the force and the energy balance to infer relations between plasma-beta
and free magnetic energy, to study the direction of currents in the corona with
respect to the magnetic field, and to estimate the errors in the free magnetic
energy by neglecting effects of the plasma (beta<<1). A comparison with a 3D
MHD model supports our basic considerations. If plasma-beta is of the order of
the relative free energy (the ratio of the free magnetic energy to the total
magnetic energy) then the pressure gradient can balance the Lorentz force. This
is the case in the solar corona, and therefore the currents are not properly
described. In particular the error in terms of magnetic energy by neglecting
the plasma is of the order of the free magnetic energy, so that the latter can
not be reliably determined by an extrapolation. While a force-free
extrapolation might capture the magnetic structure and connectivity of the
coronal magnetic field, the derived currents and free magnetic energy are not
reliable. Thus quantitative results of extrapolations on the location and
amount of heating in the corona (through current dissipation) and on the energy
storage of the magnetic field (e.g. for eruptive events) are limited.
