We estimate upper limits on the magnetic energy density in the compact X-ray emission region of the Seyfert galaxies NGC 4051 and NGC 6814 and the quasars 3C273, 3C279 and H1821 + 643 using synchrotron self-Compton theory. The size of the emission region is obtained from the X-ray variability time-scale, and the electron density from the assumption that the X-ray emission in AGN is due to non-thermal Comptonization of soft 'blue bump' photons. The competition between synchrotron self-Compton emission and direct Comptonization then enables us to estimate the relative importance of the magnetic and radiation fields. Equipartition between magnetic and X-ray energy density is at best only marginally possible and in several cases is strongly ruled out. This poses serious problems for many theories for the acceleration and radiation of particles in the X-ray emission region. We discuss several alternative pictures that do allow equipartition to occur. The most promising model, suggested by the work of Rees, paradoxically requires the magnetic field to be strong. It then confines many small, dense, clouds in the region which cause the optical and UV photosphere to lie beyond the X-ray emission region. The primary radiation is then synchrotron self-Compton emission.
