  X-ray binaries and AGN show observational evidence for magnetized hot
plasmas. Despite years of data, very little is known on these {\it coronae}
especially on the mechanisms responsible for their heating, and most models
simply assume their existence. However, understanding its properties has now
become a key issue of the AGN and microquasars modelling. Here we consider the
effect of a strong vertical magnetic field on the corona AGN and X-ray binaries
and show that its modeling (structure, heating) must be reconsidered. As a
first step, we present one mechanism that could extract energy from the
accretion disks and deposits it in the coronae: the {\it magnetic pumping
