Аннотация:The thermodynamic potential (TDP) of the boson sector of the Weinberg-Salam model in an external uniform magnetic field at finite temperature and nonzero chemical potential is calculated in one-loop approximation. In the high temperature limit with the use of Mellin summation technique explicit expressions for the thermodynamic potential are obtained to analyze its new minimum, different from the ordinary Higgs one. This new minimum is due to the root singularity in the one-loop expression for the TDP, originating as a consequence of the tachyonic mode in the spectrum of gauge boson in the magnetic field. It is demonstrated that in the high temperature limit the Higgs minimum possesses properties common with the ordinary superconductors and Abelian Higgs model. The influence of the magnetic field on the Higgs minimum is indirect and has a sufficiently complicated character. The presence of the nonzero chemical potential lowers the critical temperature leading to the disappearance of the Higgs minimum.