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A model is developed to describe the electrostatic boundary layer in a positively biased magnetic filter in filtered arcs with low collisionality. The set of equations used includes the electron momentum equation, with an anomalous collision term due to micro-instabilities leading to Bohm diffusion, electron mass conservation, and Poisson equation. Analytical solutions are obtained, valid for the regimes of interest, leading to an explicit expression to determine the electron density current to the filter wall as a function of the potential of the filter and the ratio of electron density at the plasma to that at the filter wall. Using a set of planar and cylindrical probes it is verified experimentally that the mentioned ratio of electron densities remains reasonably constant for different magnetic field values and probe bias, which allows to obtain a closed expression for the current. Comparisons are made with the experimentally determined current collected at different sections of a positively biased straight filter.