I read that the characteristics of the force field was that it could be turned on and off within the ship, that it appeared when a projectile approached and then disappeared, that it could distinguish between friend and foe objects.
One thought was that it was velocity based, ie fast projectiles were stopped but slow moving ones were not.
Bottom line is you're talking about a somewhat intelligent force field system which can detect whether an approaching object is a friend or foe and then decide to deploy the field. While we have AI based systems that can do a variety of tasks, they are probably too slow to react to any fast moving threat.
There is no general force field in physics that we know of that can repel any object at the scale of ID4. We do have electromagnetic fields but they would only act on certain types of objects with charges or magnetic properties.
Stargate SG-1 The Nox episode showed that the Gou'ld bad guys had a personal force field that reacted to fast moving objects but allowed slow moving ones to enter.