Q.Which charge configuration produces a uniform electric field?

For an infinite flat sheet carrying uniform surface charge density sigma (charge per unit area), applying Gauss's law with a small pillbox-shaped Gaussian surface straddling the sheet (two flat circular end caps of area A each, parallel to the sheet) gives 2EA = sigma A/epsilon0, so E = sigma/(2 epsilon0), independent of distance from the sheet -- a genuinely uniform field on either side, unlike the fields of a point charge or a line charge, both of which weaken with distance. When two large parallel sheets carrying equal and opposite surface charge densities +sigma and -sigma are placed close together, their individual fields add in the region between the sheets (giving a combined field E = sigma/epsilon0 there) and exactly cancel outside the pair, so the net field is confined entirely to the gap between the two sheets -- precisely the idealised configuration used to model the interior of a parallel-plate capacitor, whose own capacitance formula (see Parallel Plate Capacitance and Plate Separation) is built directly on this result.