Three-dimensional simulations of the trajectories of secondary electrons (SE) in the scanning electron microscope have been performed for plenty of real configurations of the specimen chamber, including all its basic components. The primary purpose was to evaluate the collection efficiency of the Everhart-Thornley detector of SE and to reveal fundamental rules for tailoring the set-ups in which efficient signal acquisition can be expected. Intuitive realizations about the easiness of attracting the SEs towards the biased front grid of the detector have shown themselves likely as false, and all grounded objects in the chamber have been proven to influence the spatial distribution of the signal-extracting field. The role of the magnetic field penetrating from inside the objective lens is shown to play an ambiguous role regarding possible support for the signal collection.