We study the synchrotron radiation of gluons by fast quarks in strong magnetic field produced by colliding relativistic heavy ions. We argue that due to high electric conductivity of plasma, the magnetic field is almost constant during the entire plasma lifetime. We calculate the energy loss due to synchrotron radiation of gluons by fast quarks. We find that the typical energy loss per unit length for a light quark at the Large Hadron Collider is a few GeV per fm. This effect alone predicts quenching of jets with p⊥ up to about 20 GeV.We also show that the spin-flip transition effect accompanying the synchrotron radiation leads to a strong polarization of quarks and leptons with respect to the direction of the magnetic field. Observation of the lepton polarization may provide a direct evidence of existence of strong magnetic field in heavy-ion collisions.