A thin current sheet (TCS), with the width of an order of thermal proton gyroradius, appears a fundamental physical object which plays an important role in structuring of major magnetospheric current systems (magnetotail, magnetodisk, etc.). The TCSs are nowadays under extensive study by means of space missions and theoretical models. We consider a simple model of the TCS separating two half‐spaces occupied by a homogenous magnetic field of opposite sign tangential to the TCS; a small normal component of the magnetic field is prescribed. An analytical solution for the electric current and plasma density in the close vicinity of the TCS has been obtained and compared with numerical simulation. The number density and the electric current profiles have two maxima each. The characteristic spatial scale zS of the maxima location was investigated as a function of initial pitch angle of an incoming charge particle. The effect of the thermal dispersion of the incoming proton beam have been taken into consideration. Key Points A new analytical solution is found Analytical solution was compared with the numerical simulation The new scaling is found