In this paper we consider the motion of a hot plasma in an electromagnetic field, on the assumption that the ions are at rest, that the effect of the electron-ion collisions is negligible and that the action of the electrons is equivalent to an isotropic pressure. On the supposition that a shock wave forms in the plasma, we establish the equations of discontinuity, through the shock layer, relative to electron velocity and density and the electrical and magnetic fields. The results obtained are applied to the case of a plane shock wave that advances in a plasma at rest, and we determine the cases and conditions in which a shok wave can arise.