Langmuir probe diagnostic on magnetic plasma devices often encounters more challenges in data processing than in non-magnetized plasmas, the latest itself being far from simple. In this paper, a theory of particle collection by a probe at the plasma potential in collisionless weakly ionized plasmas is constructed, accounting for velocities distributed according to the Maxwell equation and different mechanisms of particle collection depending on their speed. Experimental validation of the presented theory has been done with 2 cylindrical probes (r_pr = 75 mum and L_pr = 1 cm and r_pr = 0.5 mm and L_pr = 1 cm) parallel to B --> on a linear plasma device Aline, with magnetic fields of 0.0024-0.1 T and plasma densities of 10¹⁵-10¹⁷ m^-3 in helium. Cylindrical probe measurements are compared to data from a planar probe perpendicular to the magnetic field, and the results for electron density, temperature, and plasma potential are presented. The introduced theory is initially constructed for a cylindrical probe but is applicable to various probe sizes, shapes, and orientations. Alongside the main subject, a number of associated issues are addressed with different details: a probe design issue relative to the magnetized environment, the "intersection" method of plasma potential evaluation, and the robustness of the conventional "1st derivative" method, a current bump near the plasma potential, lower limit for electron temperature estimation, and self-consistent calculation of electron temperature and density.