BTW, Jon is correct in post #12 here.
The definition of f/stop is 'focal length divided by aperture diameter'. For a 200 mm f/4 lens, it would mean that the entrance pupil has to be large enough to accomodate a 50 mm lens diameter (200/4). You cannot have a smaller entrance pupil than what's dictated by the maximum aperture of the lens. Otherwise, my 400/2.8 would be the size of a 400/5.6.
And it matters not how large or small your sensor is - the same rules apply to APS-C, 35mm, medium format, and tiny P&S cameras.
Oddly, at the wide-angle end of the spectrum, the entrance pupil is generally larger or much larger than the lens aperture would dictate. This is because the angle-of-view requires the ability to collect light way off of the center axis. The 15 mm fisheye is a good example - the entrance pupil to the lens is much larger than 15 mm, yet the f/stop is only f/2.8. Why? Because the lens has to "see" much wider (180-degrees corner to corner on full-frame). Ultrawides are similar, but to a lessor extent.
So why do we have EF-S lenses in the first place? Because of the backfocus distance primarily, and because on wider lenses, we can get away with smaller diameter glass in the back end of the lens. Consider this - the backfocus distance for an EF lens (distance from the back flange of the lens to the sensor/film) is 44 mm. It's the same on an EF-S lens but the EF-S lens allows the lens to protrude into the mirror box a few mm more. What does this mean? Consider that any lens shorter than 44 mm has to have additional correctional lens elements (retrofocus or 'inverted telephoto' design) to create a focal length that is shorter than the distance from the back of the lens to the sensor. And the shorter the lens focal length, the more correction is necessary. By shortening that backfocus distance (as is done on the EF-S lens), the amount of correction necessary is reduced allowing (at least in theory) for somewhat better image quality.
This is not a problem on longer lenses where often times, the rearmost element of the lens is several mm away from the mounting flange.