  Most astrophysical sources powered by accretion onto a black hole, either of
stellar mass or supermassive, when observed with hard X-rays show signs of a
hot Comptonizing component in the flow, the so-called corona, with observed
temperatures and optical depths lying in a narrow range (0.1 < \tau < 1 and
1x10^9 K < T < 3x10^9 K). Here we argue that these facts constitute strong
supporting evidence for a magnetically-dominated corona. We show that the
inferred thermal energy content of the corona, in all black hole systems, is
far too low to explain their observed hard X-ray luminosities, unless either
the size of the corona is at least of the order of 10^3 Schwarzschild radii, or
the corona itself is in fact a reservoir, where the energy is mainly stored in
the form of a magnetic field generated by a sheared rotator (probably the
accretion disc). We briefly outline the main reasons why the former possibility
is to be discarded, and the latter preferred.
