Observations show that the magnetopause can sometimes be represented as a tangential discontinuity in the magnetic field. In this paper, we use a theoretical model of steady-state tangential discontinuities to analyze the microscale structure of the nose of the magnetopause. The boundary layer is described in terms of a kinetic theory based on the Vlasov-Maxwell equations for the charged particles and electromagnetic fields. The general model represents the magnetosheath and magnetospheric sides as distinct regions with anisotropic displaced Maxwellian equilibrium states and allows the presence of a multi-component plasma whose ionic species have different concentrations, temperatures, anisotropies, etc. For the nose region, we assume for simplicity an isotropic Maxwellian Hydrogen plasma. Transition profiles for the magnetic field, electric potential, electric field, charge separation and density are illustrated. The variations of the magnetic field direction in the discontinuity plane show a great variety of rotational structures in accordance with recent observations. The electric potential difference is seen to control the thickness of the magnetopause. The classical Ferraro boundary layer where the ion current is neglected is recovered when the ion distribution function is a Maxwellian everywhere in the transition. When there is no electric potential difference across the sheath we find again an 'electron-dominated' boundary layer where the electric current is mainly carried by the electrons. However, computations of drift and thermal velocities indicate that a two-stream instability occurs in the centre of these sheaths. The result will be a broadening of the layer by wave-particle interactions leading to an 'ion-dominated' transition.