  In an external magnetic field, the energy of the electroweak
sphaleron---representing the energy barrier to baryon and lepton number
violation---decreases but remains nonzero until the upper Ambjorn-Olesen
critical field strength set by the Higgs mass and the electric charge, where it
vanishes. We demonstrate this by numerically computing the sphaleron
configuration in the presence of an external magnetic field, over the full
range of field strengths until the energy barrier vanishes. We discuss the
implications for baryogenesis in the early universe, and the possibility of
observing of baryon and lepton number violation in heavy-ion collisions.
