existence of other forces obeying inv square law Is there any restriction in what we know of physics to the existence of other type of forces that obey the inverse square law in 3 dimensions.
I mean other than electromagnetic and gravitational.
Also if there were some other kind of force ..would it follow that it would have a dual like electric and magnetic forces are duals of each other.
 A: A $1/r^2$ force occurs because the particle mediating the force is massless. The only way there could be another such particle that had not yet been detected would be if the coupling constant for this force was small or zero for ordinary forms of matter. For example, suppose that we, our world, and our lab apparatus were all made out of neutrons. We might have a very hard time learning of the existence of the electromagnetic force. (Neutrons do have a magnetic moment, though.) I could imagine, for example, that dark matter possesses some new type of charge (not electric charge) that is zero for baryonic matter.
Re duals, these are general features of all fields due to the way special relativity works. For example, there is a standard, easy argument http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html#Section11.1 that if we have electrical interactions plus SR, we must have magnetic interactions. However, the detailed nature of the dual depends on the nature of the field equations, or, in QFT terms, on the spin of the force-carrying particle. For example, the graviton has spin 2, not spin 1 like the photon, so we don't have a dual structure exactly like (E,B) in E&M. There are, however, some very nice analogies between the (E,B) structure and what you see in stationary fields such as that of the rotating earth. GR does have phenomena that people refer to as "gravitomagnetism," etc. But the analogy is not perfect, because otherwise GR would be the same theory as E&M. The fundamental reason for the difference is the spin of 2 instead of 1.
A: The $1/r^2$ behavior is characteristic of a massless particle mediating the interaction. For electromagnetism, that particle is the photon, while for gravity it's the graviton. When an interaction is mediated by a massless particle, then it is of infinite-range. For example, two electrons will repel each other regardless of how far they are (as long as they are in causal contact of course). Another force that behaves like $1/r^2$ would have to also be of infinite-range, and so very easy to observe, unless it was extremely weak. So, most likely, there are no other $1/r^2$ forces.
A: No, there's no reason that the electromagnetic and gravitational forces necessarily have to be the only ones with $\frac{1}{r^2}$ dependence. Or rather, there's no reason that we know of, and I don't think there are any theories being seriously considered that do predict those to be the only two inverse-square-law forces. They are simply the only ones that have been observed. (Note that gravity is actually not quite an inverse-square force once you take general relativity into account.)
If another inverse-square force did exist,it would not necessarily have a dual force, the way the electric and magnetic forces do.
A: I would add that in Grand Unified Theories where the unification happens at very high energies, there exist a number of mediating particle X Y etc for forces consistent to  the SU(2)XSU(3)xU(1) low energy structure which in the high energy limit before symmetry breaking are massless and similar to the photon, i.e. of 1/r^2 behavior. Even gluons themselves. More so if one includes supersymmetry in the brew.
The verification of the existence of these forces is  an aim of the HEP experiments.
