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

We report on ROSAT HRI observations of the nearby powerful radio galaxies 3C33 and 3C111, which both have detected optical hot spots. We find nuclear X-ray sources in both objects, but no X-ray emission from the hot spots. This confirms the presence of a high-energy cutoff 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 hot spots 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.