A simple model of a nanofluidic transistor consisting of a uniformly charged central section between a pair of plane parallel walls is considered. The linearized Poisson-Boltzmann equation corresponding to weak surface charge is solved exactly, and the solution is presented as an infinite series. The problem is characterized by three dimensionless parameters, namely the normalized surface charge, the ratio of the channel width to the Debye length, and the length-to-width aspect ratio of the charged section. The first of these parameters is presumed small, but the other two are arbitrary. The dependence of the exclusion-enrichment effect on these three parameters is discussed.