Magnetic field strengths in the hotspots of 3C 33 and 111

We report on ROSAT HRI observations of the nearby powerful radio galaxies 3C 33 and 111, which both have detected optical hotspots. We find nuclear X-ray sources in both objects, but no X-ray emission from the hotspots. This confirms the presence of a high-energy cut-off in the spectrum of synchrotron-emitting electrons. Since these electrons necessarily scatter the synchrotron photons by the inverse Compton process, our upper limits on the X-ray fluxes of the hotspots allow us to set lower limits of a few nanotesla on their magnetic flux density, close to or greater than the fields implied by equipartition of energy between radiating particles and magnetic field.