  The presence of a primordial magnetic field in the early universe affects the
dynamic of the electroweak phase transition enhancing its strength. This effect
may enlarge the window for electroweak baryogenesis in the minimal
supersymmetric extension of the standard model or even resurrect the
electroweak baryogenesis scenario in the standard model. We compute the
sphaleron energy in the background of the magnetic field and show that, due to
the sphaleron dipole moment, the barrier between topologically inequivalent
vacua is lowered. Therefore, the preservation of the baryon asymmetry calls for
a much stronger phase transition than required in the absence of a magnetic
field. We show that this effect overwhelms the gain in the phase transition
strength, and conclude that magnetic fields do not help electroweak
baryogenesis.
